My soon-to-be spouse just PCS'd and my current unit is about to go on rotation. Could she get attached to my unit for a the rotation?

It depends. Looks like you are in a AVUM or AVIM associated unit. It depends what MOS your fiancé is and what the needs of the unit are. When you say, "rotation," I assume you mean a deployment, not a CTC rotation. Usually, a MTOE unit will only be deployed if its readiness is high enough to meet the requirements of the mission. This means that it already has all the people that it needs. You can't get attached to a unit that already is at 100% of its requirement for personnel based on the limit placed on the theater. I'm sure you've heard that there's only a certain amount of "boots on the ground" there. Your unit makes up a portion of that and they aren't allowed to go over that number. Also, since she just PCS'ed, the likelihood of the new unit releasing them is highly unlikely. Even if you were married, they PCS'ed to a new unit. They aren't going to take a hit on their books so that you two can share a CHU in Iraq/Syria/Afghanistan or wherever. If they are in a unit that normally deploys individuals however, there is a chance. If they are in a normal MTOE unit...not going to happen.

"Soon-to-be" doesn't mean anything. You are either married or single in the military. After you are married, you may be able to have both of you assigned to the unit. I once deployed with a couple.

No. Typically a unit will stabilize before going out, so the only ones going out are the ones who are on their roster. Any new personnel after the stabilization will be left behind typically standing duty, cleaning toilets, or loaned out to another unit until their unit returns.