It's definitely possible, but I think the dynamic you mention is more likely to be true if you're talking about a guy jumping from a lower level of competition to a higher one (e.g., G5 to P5).
If a dude is fielding successful teams at a P5 program, any P5 program, I think the chances are pretty good that he could go somewhere else and do the same thing. For example, it isn't surprising to me that James Franklin went to Penn St and has been good there, given what he did at Vandy. It isn't easy to recruit to Iowa St, and they are a middle-to-bottom tier program in that conference, but he's gone 26-19 in conference play there and is 24-12 if you throw out his very first year. Came very close to winning a conference championship there this year and won a NY6 bowl.