Was the Caribbean Sea a closed sea during the last glaciation? Taking a look at Google Earth the straits between the Caribbean Sea and the Atlantic Ocean are not very deep.

The sealevel during the last glaciation was 120 meters lower than the present level.
Was the Caribbean Sea a closed or semi-closed sea during the last glaciation or the straits were deep enough to make it a connected sea?
Thanks to @Eartworm I learned today I was totally uncorrect: there are more than 2000 meters deep in the straits.

Tool to see bathymetry, navionics.com