I do. Again, not necessarily "a draw" per se, but I think it matters when players visit. Sitting across from him and talking football has been something quite a few players have commented on, and he's been a guy who has sold several on coming here. Without that, or the clout he carries, even if we as fans might be critical, I think makes things challenging.
As I also said in another post, the challenge I think they might have with Mayo is he has no real weight outside of the Patriots. You look at any other coach in the league, they all came from somewhere and worked with other guys, so there's that sort of networking that exists when it comes to player relationships and endorsements that those guys would garner that Mayo wouldn't.
The thing that also complicates the situation is you usually have either a coach or a QB who can be sold to players, especially top-flight receivers, during free agency. Those guys generally also want to be productive with whoever they sign with, so they can put up numbers and put themselves in a position for the future to get their next contract. We're in a situation where they may not have either (coach or QB) after this season. Without Belichick and with an unknown (or another rookie) QB, that absolutely hurts their chances. Unless they're willing to overpay, which even with Bill gone, probably won't change.
If that happens, it just leaves them where no amount of cap space is quickly going to fix this. And as we all know, building a young nucleus on that side of the ball is going to take years, which likely means a few more seasons of this. Which obviously is going to be tougher than people probably think for all of us to live through.