I haven't done it with Marriott, but have with Hilton (so take this with a large grain of salt). In that case, all nights counted towards the year in which I checked out. This results with me having 5 night credits 2 nights into the year... Again, haven't done it with Marriott but I wouldn't take it for granted that the December nights will count towards this year if you check out next year.

If someone that has done it posts otherwise of if there's reference in the T&Cs, that should be definitive.