No. I believe hamsters are native to the desert, and they clean themselves, so this seems resembling a bad idea. Also, if you vanished it unattended, it could easily drown. Also, it might catch hypothermia if it doesn't achieve dried well (that's pure conjecture, though.) I wouldn't risk it.
Answers: only bath your hamsters if it is desparate (it smells really bleak or stuff like that)... they are tiny animals that do lose body heat FAST and its more hassle than its worth. and they also lose body oils that they entail each time you give them a bath.
you wouldnt be capable of use soap anyway so theres really no point.
it is a good idea to put a bowl of marine on the cage but not full to the brim cos at the end of the day it will a short time ago tip it over. during the winter though make sur that the room that its in is warm adjectives the time