Shouldn't (but will in all likelihood) get points for both. It may be worth asking the hotel first if they'd be willing to let you check out a night early without paying for the last night. I've found a lot of hotels are pretty flexible in that regard so may be worth a shot.

If they aren't willing to or you aren't comfortable asking , I would avoid checking out and settling F&B the night before if at all possible. It's easy enough to call and handle all of that over the phone if there are any issues. Officially checking out early seems like such an easy concept, but this has created issues for me in the past. I've been refused points for the entire stay with the hotel saying I was a no show, been charged a full cancellation penalty, and had my rate increased for the other nights.