Here are a couple of maps of the currents in the Gulf.
The Loop Current :
http://oceancurrents.rsmas.miami.edu/atlantic/loop-current.htmland the Yucatan Current :
http://oceancurrents.rsmas.miami.edu/caribbean/yucatan.htmlOne feeds the other for the most part. Looking at the maps there doesn't seem to be a lot to worry about from a "current" perspective given that all of the arrows pretty much point away from Cancun (from the current spill perspective) but one line from the Yucatan Current info did raise an eyebrow ;
"Ochoa et al. (2001) were the first to report a mean southerly flow on the eastern side of the Yucatan Channel between 500 and 1500 m depth. They speculated that the 2 Sv of water it transports are the recirculation of waters of the same depth that enter the Gulf of Mexico as the Loop Current. The water that cannot flow out of the gulf through the Florida Straits apparently returns to the Caribbean Sea in this fashion."
This to me says there is obviously some chance of spillage (of water) back into the Caribbean sea although on the Cuba side as opposed to the Mexican (Cancun) side . . .