They do have a frequent guest program. There's not any information online from what I can tell, but to get a number, go to the morgans hotel group website and create a profile. When you finish it will assign you a number. Don't do what I did and not write it down. LOL. I didn't do it and trying to retrieve the number isn't easy. I just called their reservation line and they can't find an account for me, yet when i log in I can see some of my past reservations. Their solution was to log in and create a new profile and write down the number. I have an upcoming stay this weekend so I'm going to hold on creating a new profile and just ask the desk if they can pull up my number.
As far as benefits go, I don't know what they are. If I get more info this weekend, I'll update this thread.