There have been times when I've called a hotel and said that I left early in the morning and wasn't sure whether I'd come back so I'd taken my luggage with me, now I know I won't come back, and asked whether they can check me out in my absence and mail me the folio. I've never had a problem with that.

Actually, I've only ever done this when it was in fact true, but it should work for you as well. Myself, I wouldn't just not show up and assume they'd check me out on time.