It was clear when we got our offer what team we were signing up for. I wouldn't do it - seems like a bad start for a team, OP. Have you asked? If you have and they still won't tell you, seems fishy.

Not normal

When you say register, do you mean committing financially? I would be wearing to fork over money if you don't know if you're on A or B team. If this is the situation, this is NOT normal/common.

Typically when this happens the program hasn't filled out the roster for the A team. A sign of this is if the program adds additional tryout dates or open gyms.

Is it common for a program to ask you to register before telling you if you made the A or B team?