I really don't think the timing of the hire is all that important, so I'd say that waiting until after the bowl game would have little effect on whether I think a hiring process was botched or not. Alabama had to wait a while to get Saban, and I don't think they botched that one.
If Byrne makes a good hire, that's the most important thing, not the timing. Whether you make a hire today or a month from today, this recruiting class will still be a transition recruiting class, so I don't see why the timing is all that important.