No, but when the league consists of many players who are signed to NHL contracts, that would be considered a professional league. It's happened with
players coming over from Europe as well.
It is, and there are plenty of NCAA rules that are sillier than that. But if you play in a league that provides financial compensation to players and allows them to play after signing NHL contracts, it's hard to argue that you don't play in a "professional" league.
I do want to clarify this: I am not cheerleading for the NCAA nor am I saying that they don't have some rules that are beyond silly, but I'm just explaining their reasoning.