Some random thoughts, based on the comments I've read here.
No, not all HBCU's would be in on this. I can see a 16-team league, and the organizers would have to choose their markets carefully. Urban areas with no NBA presence. I could see Norfolk State getting in on this. I'll put it to you: if you lived in the Norfolk area, and Norfolk State put together a pretty good team (guys who might have gone to Duke or UNCheat instead), would you go to watch them play? I would. Howard or Morgan State, OTOH? Probably not, unless there was something exceptional about the team that caught my attention.
Just a bball minor league? No. Minor league bball always fails because they can't develop a fan base. Places like Grambling have fan bases.
Would the NCAA kick the participating schools out for all sports? They might try, but it would end up in court, and the NCAA would probably lose. I wouldn't be surprised if the NCAA changed the rule allowing players to be a pro in one sport, and amateur in others. That would probably end up in court, too.