No, he forgets.

Dreams often fade, the memory of the night banished by the morning sun either into the back of the mind or back into the void they came from. Even in a world where dreams can be more then just the mind dealing with the daylight thoughts of living. So the question is, had Peter forgotten the dream which held the information which would reveal his new 'truth'.

The answer was yes. As the dream ended and began to fade, he wasn't sure if it was real or not. Which caused him to lose the memory, even if he still received the gift. A gift he didn't know that he had, which meant that he wouldn't know he was using.

So Peter prepared for his day. A day of working whether in the field as a hero or at one of the jobs he had managed to get over his life time. Photographer, teacher, research scientist, billionaire company owner, and any number of others. A day of meeting friends, family, enemies, and rivals. A day of heroes, villains, and ordinary people living their lives.