bbPress and WPMU

Since there's a theme for bbPress on this site I'm guessing that bbPress works well with WPMU.

My question, though, is: Can each user have his/her own bbPress forum with the bbPress plugin?

I want to be able to have a main forum (on top domain) where all bloggers can post. I also want each user to be able to create his or her own forum and have users register to that forum.

It would be cool if all the users were from the same database, so that a user on a.site.com could also post on b.site.com's forum with the same username, avatar etc.

Is that how bbPress works? If not, is there a forum plugin like that?