It's definitely an interesting factor that I wouldn't have considered, and as you mentioned getting some of their recruits in and on the field contributing immediately is definitely plays into that success.
Another factor with the first term coach, just has to do with the energy and enthusiasm they can bring to a program, especially one that is down or hit hard times. Think about the some of the programs those coaches came into and started winning immediately: Oklahoma in the 10 years prior to Stoops was 61-50-3; LSU was 33-24-1 under Dinardo before Saban; USC was 37-35 in the six years before Carroll; Florida was 23-14 under Zook before Meyer; Alabama was 26-23 under Shula before Saban; Auburn was 33-19 under Chizik; Florida State was 27-13 in Bowden's last three years.
All of those programs had had traditional success too, so they were already getting good players/recruits, they just needed some energy and enthusiasm from a new head coach. Sounds like what *could* happen with a certain school up north.