PM involves overseeing all aspects of the project. Getting skills in one part will only help the overall ability of the PM to properly understand, budget, and manage the different parts.
Personally BA covers the scope and product alignment to the client needs. I think this is a huge skill set that every PM needs at least a little experience with in order to properly do their job. It's important to have experts, but if this is out of school and going into the field this will only strengthen her ability and references for becoming a PM.
Note: The issue comes when one stays extremely long in a very specific field and then wants to jump over. So if she stays for 7-10 years as a BA and then wants to just jump into PM without training then her skills might be viewed as one sided, but it sounds more like she has solid schooling and is looking for experience, which if that is the case the BA is a solid move in that direction. Get a couple years and then swap it up to PM or another role in the SDLC to round out the experience.
P.S. I would check options at role rotations in the place the BA position is at. It's better to get in the door and bounce to a few different roles than having to swap companies each time.