Does anything stop her from finishing the task?

No, she makes it to the Fat Lady

Slightly out of breath, Hermione stopped in front of the entrance to her dormitory, her clothes and safety almost in her grasp.

"I take it you have the flower?" The Fat Lady asked imperiously.

Panting, Hermione held up her slightly crushed poppy. "Here," She spoke through heavy breaths. "Now let me in!"

"No."

Hermione's heart dropped. "What do you mean no! I brought you the flower!"

"The flower was only part of the task, you silly girl!" The Fat Lady said. "The task is that you must eat the flower in front of the one who dared, you, remember?"

Hermione stopped for a moment. She did remember that part, now, yes, but she didn't know what the flower did... "I don't suppose... You know what this flower is, do you?"

"I do."

"What is it?"

"I'm not going to tell you until you eat it."

"What!? Why not?!" Hermione stammered, incredulous that a painting would keep such important information from her. For all she knew, the flower could kill her!

"Many who did this challenge had no idea what flowers they were eating until it was too late. I've seen many witches get taken to the hospital wing, but many more be perfectly fine. However," she continued, seeing the panic on Hermione's face, "I will assure you that the flower you possess will do no lasting harm to you. It will not require you to visit the hospital wing, and any effects it has on you will be over within an hour."

That... didn't seem all that bad, considering. "If I eat the flower, will you open up?"

"I will allow you through as soon as you can get through the hole, "The Fat Lady promised.

Well... It was better than nothing. Hermione weighed her options. All she'd have to do is eat the flower, then she could make her way toward the hole as fast as she could and hope to make it up the stairs before anything bad happened. On the other hand, the Fat Lady hinted that the flower could incapacitate her.