I doubt they'd bother - if they were specifically wanting tower or approach that's who they'd hire.
Yes, one would think that. However, this is AsA we are talking about.
A recent foreign hire who I worked with, went with no approach experience. Hired on for tower, allegedly. When he arrived he was given an approach course and now sits in an approach seat.
I suspect they don't let this sort of information out to the troops. "Back-fill", and all that.