Not at all. The US dollar is common currency on Coz. *How's that for alliteration?*
The smartest thing to do is take a lot of $1 bills along. They take up space, but are quite useful.
You can exchange US for pesos almost anywhere. In restaurants, etc. ask for "la cuenta" (the bill) in US as well as in pesos.
Here's some Cozumel info that you may find helpful ...
Let us know if we can help more !!!