He can, assuming he is available and wants to.
John Wildhack offered Coach Babers the opportunity to coach the Wake game AND a possible bowl game.
That tells me he is thinking the new coach is not going to coach the bowl game.
It would be asking a lot of a coach to bring him in out of the blue, not knowing any players, probably not familiar with the schemes Syracuse is using, maybe not even knowing any of the assistants, and ask them to coach.
I think it would be better to have the new hire focus on lining up a new staff, work on evaluating and hopefully solidifying existing recruits, adding some additional ones and perhaps most importantly, work on retaining our players and adding some more from the portal.