Wherever you stay, you can be assured that your membership and its benefits will be recognized.
This is the statement on their site - Maybe we should ask which benefits are recognized. Here is a link to peruse around on to get details. http://www.ritzcarlton.com/en/Rewards/AboutRewards/MarriottRewardsPartnership.htm
I don't think Ritz and Marriott are seamlessly on track yet though at some properties. I am having trouble in Singapore. They do not recognize Marriott Rewards there.
I don't see anthing referencing Marriott Cheques on their site yet - just the Certificate use and redemption policy.
No. Certificates that have already been ordered will be honored for upcoming reservations, and must be presented upon check-in. http://www.ritzcarlton.com/en/Rewards/AboutRewards/Questions.htm