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Well, the distinction between a “sea” and an “ocean” is quite fuzzy already. The Caribbean is directly connected to the Atlantic in quite a number of places as it is — compare this to the Mediterranean Sea, which connects to the Atlantic at exactly one point, namely the Straits of Gibraltar.
The Caribbean is considered to be a distinct sea mainly because there are a good number of islands and island chains separating it from the Atlantic and creating local conditions (currents, etc.) that are sufficiently different from the rest of the North Atlantic to justify a unique designation. And also, I’m sure, quite a bit of nautical tradition.
So, basically, a lot more would have to change for the Caribbean to lose its oceanographic status as a sea than just these rocks wearing away.
On top of which, as far as I can tell, the Bahamas aren’t technically considered to be a boundary of the Caribbean Sea in the first place. The official boundary is defined to be significantly further south, at Cuba.
Sources: Wikipedia, basically