What I mean is, you probably won't have to worry about getting it down to the day. I.e., it's delayed a month--you won't have to worry about not having a car for that time.
As far as the logistics--sure, you'll be signing a lease on the day you turn it in, so there's nothing special there. You'll definitely need to talk to the dealer, though--they can basically say or do whatever they want, provided there's a contract (and it's in their favor).