At some point there is no longer a connection. I would say after five years recruiting squarely falls on the shoulders of the new coach and the success, or failure, of a program does as well.
I think Miles is closer to Fulmer than Saban. He can recruit (but that isn't as hard in a talent rich state with only one major university), but when all else is equal he gets out coached. His luck has usually been made by talented players, not by talented coaching.
So the answer to your question is that yes, Miles inherited a program on the rise a decade ago. But, The team is now firmly his responsibility. Personally, I don't see him winning a national championship there but due to solid recruiting he will continue to have a Fulmer like level of success, complete with a slow deterioration as the game continues to evolve.