How recently? At one time most HA rooms were only a King and therefore to accommodate a family a connecting room was required -- those were labeled "king + queen" or something. That room type is no longer offered as of a few years ago. All resorts, including ASMu, now offer wheelchair accessible rooms with 2 queens. You should be assigned the exact HA room type that you booked (i.e. beds and shower vs tub).
HA rooms are not restricted to the ground floor as long as there is an elevator, and all buildings greater than 3 stories must have an elevator. That is most WDW resorts with the exception of CBR and some buildings at OKW. In the event of an emergency Reedy Creek knows exactly where the wheelchair-accessible rooms are located. If it helps your peace of mind, next time you can ask at the front desk whether you should stay in your room or some resorts apparently now have a designated "wheelchair meeting location" in the event of evacuation.