I think BA's in general can move towards PM roles with additional education (formal or informal) and initiative.  Having an MBA background will also give you a good base from which to get into the PM world.

It's not an automatic transfer though - it all depends on your skill set and how BA's are perceived in your area.  I know some firms in my area typecast BA's into very limited roles and they don't get the exposure to the overall project that would help them move into a PM role.  But if you get to work somewhat closely with PM's while doing your BA work you can pick up a lot through osmosis and discussions with them at lunch, etc.