No. And I hope the reincarnation thing was a joke. Pegadus is a character in GX series as well and if the two were related it would have been mentioned. Aster is not a mere duelist. He is a pro duekist as in sponsored.
I mean look at the similarities. The laugh. The ego. The destined talk about his father who made heroes card specially for him. Pegasus obsessed with cartoons that usually have heroes. Dress sense. Mythically named.
Maybe Pegasus's real name is Pegasus Phoenix...a double mythical hit.