While traveling the ocean with my cat it began to make sounds (bad sounds) and then drowned. 

To see if it was a random chance or an issue with traveling over the ocean (or just with cats) I loaded up a flat world to test this bug.

I filled up three pits of water. The 1st one block deep, the 2nd two blocks deep, the 3rd very long and two blocks deep. I filled all boats used with cats and entered said boats and entered the water.

The 1st and 2nd pit I used as stationary tests to see if it was possibly a water depth or movement issue. Neither cats in the 1st and 2nd pit of water died and so I left them there while I tested in the 3rd pit. I left them there the entire time (a good few minutes) and they were still alive.

In the 3rd pit I put in the cat, got in the boat, and road it into the water as I had done with the first two. Then I took off (the pit was very long and for similar results I suggest you make a long one too). The cat died. Well, to see if it was just cats I used two slightly similar sized animals. One a chicken the other a wolf (tamed). Both the chicken and wolf survived pit 3 so I guessed they would have done the same in pit 1 and 2 and didn't test them there.

So by the little test I feel that I can reliably report that cats drown in boats while moving continuously for long distances. I did notice that the cats when in the boat (when a player is also in the boat) sit at the deepest part of the boat. The deepest part of the boat is below the water line outside of the boat so there's that bit of information.