Not true. Yes, they may take their own research fellow, but this is already decided in advance for a spot and doesn't affect the other spots. A letter from a faculty member at Mt. Sinai will carry a lot of power esp. if it is a big wig in the field.
The reason it may be a waste of time is for another reason -- it's in NYC, a very popular location and it's a very strong program. So they can be quite choosy for whoever they want regardless if you're a rotator or not. The top tier programs can afford to be very choosy and often the people who match never rotated but come from really great medical schools (and of course undergrads).
I'm assuming you're talking about the Icahn School of Medicine at Mount Sinai Program site (not St. Luke-Roosevelt that recently merged with it).
