Some cats like water, some don't. The best test is to see what they think of water spraying out of a hose. If they let you get them a little wet, they might not mind it, but if it's like my cat, it just runs away like a little girl. My cat hates water, a lot, and if I ever put her in a bath, she would hate me forever and scratch me up to shit.

So I would see how your cat likes water before dropping them in a bathtub.

I can't see the harm in it, but cats do a fine job keeping themseleves clean as it is. They are very clean animals actually.