No, chao cannot drown, all chao have a vague recollection of how to swim, the ones that struggle in the water won't drown, they'll just splash really hard to stay afloat.
They are practically the spawn of Chaos. ; D
On the other hand, your character can drown, if he's too short, tails for one is succeptable to drowning. ;_;
Conquering the world, one step at a time.