Mathew, there re not that many roads on Cozumel, so you should be able to ride them all in a good session! They're about the same standard as you'd find in an Aussie country town... a few potholes and loose stone debris on the shoulder etc.
Cozumel is 50km by 15 km and has 100,000 inhabitants, so it's not like it's a bustling metropolis.
I assume you're not going to leave it leaning against a lamp post while you have lunch, otherwise I see no reason to be unduly worried about it being stolen (note: opportunistic crime is relatively high in Mexico tourist areas).
If you're concerned about the drug gang crime we read so much about, and how that might affect you.... be assured that the Cancun region is not one of the battlegrounds, and is not named as a trouble spot.
Don't take this an as endorsement of your plan (you'll need to talk to your travel insurance company about this).... it's always best to leave really valuable items at home when you go travelling. We're usually talking about watches and jewellery when we say that, but it applies to expensive triathlon bikes too. If you're that concerned about it, it may be best to leave it locked up at home and see if you can rent or borrow a bike over there.
Phil at the safety hub about 5 years ago