Ichigo could be a sort of mediator. Given his transcendent nature, he might have a different perspective on the conflicts between the devils, angels, and fallen angels in High School DxD. He could use his powers to try and bring about peace or at least a truce among them. For example, if there's a battle about to break out, he could step in and use his unique abilities to stop it. His very presence could change the way the characters interact with each other.
He could fit in as a mysterious new student. His transcendent powers would set him apart from the rest. He might initially be seen as a threat by some of the factions in the school.