I can speak with confidence... from personal experience...

Marriott will let you book as many hotels on the same night as you want. (or I've never hit any limit on reservations)

Marriott, upon account review, if they see multiple nights credited, they will (at least they did me) send you a very nicely worded nasty gram.

IE I've had a RI booked for a long time. Some nights I'm really not there. The RI property doesn't have a way not to credit a night if I'm not there... other nights I need to do a trip to another city and stay at another MI property. So far I can say I've always received the 'double' credit.

Now that I have the letter in hand, I'll ensure that I don't stay at Marriotts when I travel and just stick with my Hilton and SPG friends. Lost revenue for Marriott I guess.