I just went back and checked, and nope no case of sea-sick elephant under Caesar :-)).
But Claudius apparently appeared just in time for the fall of Colchester with an elephant for effect in 43AD. It is not reported what happened to the creature afterwards and whether he actually did anything active in the campaign. I think Claudius may have thought it sounds impressive and Alexander had them and Hannibal had them and Pyrrhus had them, and why shouldn't Claudius have them.

But, I agree it is amazing in which ou-of-the-way places on this planet you can find people who know about Rome, including a beach on the Russian Baltic sea coast!