Not quite

Aizawa hated the idea of manipulating and weaponizing any of the students in the way that was happening, even the self-risking idiot he'd ended up helping keep an eye on, and certainly not the other students caught in her wake. So would the majority of the other teachers. Unfortunately for him and his ideals, there were people outside the school who had a fair amount of pull, and who wanted to "guide" the young Izuku toward a promising future as a powerful tool in the government's arsenal.

So it was that the classes at UI were, somewhat suddenly, and without much fanfare, rearranged somewhat. No one was booted, but classes and schedules were shifted around to expose certain talents to the new special-case student more readily. In addition, support students as teams would be assigned a handful of partners from the Hero course, which made sense even without the manipulative ulterior motives, who they would work closely with outside of classes to aide each other in improving.

As a result, the ultimate makeup of class 1A ended up being:

Seat No. 1: Mina Ashido

Acid: Mina's Quirk allows her to produce a corrosive liquid from her body. She can control the solubility and viscosity of this corrosive liquid. There is a limit to how long she can produce the corrosive liquid until her skin gradually loses its natural resistance to it.

Seat No. 2: Tsuyu Asui

(Harem) Frog: Tsuyu's Quirk gives her a frog's physiology and allows her to do anything a frog can, thereby gifting her with abilities such as: Enhanced swimming abilities, Hopping at long distances, Extending her tongue up to a maximum of 20 meters (which is strong enough to lift an entire person's body weight), Sticking to walls, Ejecting/washing her stomach, Camouflaging herself, Secreting mucous with different, controlled effects: Itch inducing, Scent masking, Paralysis. This quirk is already part of Harem.

Seat No. 3: Izuku Midoriya

Harem: This extraordinary quirk permanently links the user (the "master") with anyone they bring to orgasm, pulling their quirk into the user's own pool of abilities. The harem members can no longer access their own quirks by default, but instead, the user can distribute powers at will to their Harem, though only one quirk may be active per member at any given time (with the exception of the user, who may always have this active, and up to one other). This quirk also optimizes the user to a form well suited for maximizing it's abilities on the most targets possible.

Seat No. 4: Tenya Ida

Engine: Tenya's Quirk gives him car-like engines in each of his calves, giving him incredible running speed and **** kicking power. Tenya needs to fuel his engines by drinking orange juice.
Seat No. 5: Ochaco Uraraka

Zero Gravity: Ochaco's Quirk gives her the power to nullify the effects of gravity on solid targets (living and nonliving) by touching them with the pads on her fingertips, causing them to become weightless and float. She is able to cancel the effect of her Quirk by touching her finger pads together.

Seat No. 6: Denki Kaminari

Electrification: Denki's Quirk allows him to generate electricity and cover his body in it. While he can also emit this energy over a distance, Denki has little to no control over it. Exceeding his wattage limit causes his brain to short-circuit, leaving him in a **** state for 1 hour.
Seat No. 7: Eijiro Kirishima

Hardening: Eijiro's Quirk gives him the power to harden and sharpen any or all parts of his body, causing his flesh to become jagged and rock-like.

Seat No. 8: Mezo Shoji

Dupli-Arms: Mezo's Quirk grants him a set of tentacles alongside his arms. He can transform the tips of these tentacles to replicate other parts of his body (ex: mouth, ears, eyes). The duplicated body parts are more efficient than the originals; as a result, Mezo is able to hear better, see through more angles at a time, and they grant him much higher degrees of strength.

Seat No. 9: Kyoka Jiro

Earphone Jack: Kyoka's Quirk is that she has a pair of headphone jacks hanging from her earlobes. When the jacks are plugged into something, Kyoka can channel the sound of her heartbeat into it in the form of a violent vibration attack. She can stretch her earlobes several meters. This Quirk also allows her to hear minuscule sounds and vibrations from her surroundings.

Seat No. 10: Fumikage Tokoyami

Dark Shadow: Fumikage's Quirk allows him to manifest a sentient shadow monster from his body that he can materialize and contract freely. Dark Shadow's energy is limited and can be drained by bright light. When it runs out of energy, Dark Shadow retracts back into Fumikage's body.

Seat No. 11: Shoto Todoroki

Half-Cold Half-Hot: Shoto's Quirk gives him the ability to generate ice from the right side of his body, and flames from his left side.

Seat No. 12: Toru Hagakure

Invisibility: Toru's Quirk is that her body is completely invisible.

Seat No. 13: Katsuki Bakugo

Explosion: Katsuki's Quirk allows him to secrete nitroglycerin-like sweat from the palms of his hands and ignite it on command, allowing him to create strong explosions. The more Katsuki sweats, the stronger his explosions become. If Katsuki overuses this power, his forearms will start to ache.

Seat No. 14: Momo Yaoyorozu

Creation: Momo's Quirk gives her the ability to create any non-living material/object from her exposed skin by transforming the molecular structure of her fat cells. In order to create something, she needs to understand the molecular structure of what the material/object is made of.

Seat No. 15: Hitoshi Shinso

Brainwashing: Hitoshi's Quirk allows him to put someone in a state where they are **** to obey whatever he commands. He can only activate this power when his target verbally responds to something he says. Brainwashing needs to be intentionally activated and will not take effect if Hitoshi doesn't want it to.

Seat No. 16: Ibara Shiozaki

Vines: Ibara's Quirk gives her hair-like vines that grow on her head. She can lengthen and manipulate the vines, allowing her to attack, defend and grapple. She also has the ability to detach them at will. The vines will grow back, provided her head receives proper sunlight and water.

Seat No. 17: Itsuka Kendo

Big Fist: Itsuka's Quirk grants her the ability to enlarge both of her hands to a gigantic size. With the increased size comes enhanced striking power and gripping capabilities.

Seat No. 18: Setsuna Tokage

Lizard Tail Splitter: Setsuna's Quirk allows her to split up her body into as many as 50 pieces. Each and every one of these split pieces are able to levitate and move freely through the air. Setsuna's pieces can also regenerate if they are destroyed or otherwise unusable.

Seat No. 19: Reiko Yanagi

Poltergeist: Reiko's Quirk allows her to telekinetically control nearby objects. The weight limit of her Quirk is roughly the weight of the average human.

Seat No. 20: Neito Monoma

Copy: Neito's Quirk allows him to duplicate and use another person's Quirk after coming into physical contact with the user. He is currently able to hold four Quirks at a time and can maintain any copied powers for ten minutes. After the time limit runs out, he loses the copied Quirk until he once again touches the original user.

Izuku's Support team(which also supports several other students in both 1A and 1B, including Tsuyu), consists of:
Mei Hatsume:
Zoom: Mei's Quirk allows her to make her vision zoom in on whatever is in her line of sight. If she really focuses, Mei can see things as far as five kilometers.
Tomoko Tsutsui(OC):
Analyze: Tomoko's quirk allows her to break down the quirk of anyone she sees and understand it. It's not instantaneous, and the more use she sees, the better details she can understand, but over time it's possible for her to understand things that would be impossible to get by experimentation alone.
Takako Okano (OC):
Refresh: Takako's quirk allows her to restore the energy of anyone she touches. This doesn't do anything about injuries or the effects of harmful quirks, but can bring someone from exhausted to energetic in an instant. The downside is that anyone who is exposed to this quirk will temporarily not regain energy naturally, resulting in a bad crash when the new burst of energy does eventually run out, and it can take more than a day to recover. This can be used multiple times, but the side effects continue to escalate when it is.

In addition to these changes, All Might never met Midoriya, so the villain never escaped and captured Bakugo. All Might still ends up a teacher, but it is likely that he is considering Mirio as his successor.