I didn't take an MGMAT class (Princeton Review) but you should be fine a couple weeks after the exam. I would schedule it and then if during the class you see that you're not progressing, just reschedule.

im currently taking a manhattan gmat course, as well. My test date is Aug 18 and my class ends July 31, giving me just over 2 weeks to study.

Personally, Im a cram-it-all-in studier. The reason why I scheduled it early was so that-
1) i wouldn't lag in my studying- a 1 - 2 month stretch AFTER taking a full prep course would be too dangerous for me. i would study less and not take advantage of all the time i had. i'm someone who needs to see a looming deadline in order to really kick it up in high gear.

2) the more time that goes by, the easier it is to forget. as you know from taking the mgmat course, each week you do hw on topic X, THEN reinforce the topic in class, THEN do OG problems for the same topic. This helps to really nail down the concepts, which I would probably get a little fuzzy on.

Honestly, I don't feel I'll be fully prepared for my August 18 test date, but I also scheduled one for September. That way, I have 1 shot of taking the test with the concepts "fresher" in my mind, despite more practice needed, and then another shot with additional practice.

best of luck!