Hell yeah, many Beardies love to have baths and it's also very good for them, keeps them
hydrated and helps with shedding.
I'v seen videos of some Beardies swimming underwater and i think it should be okay, aslong as they come back up
When you
bath your own you should make sure the water is not too hot or cold (kinda like a babys temperature for a
bath) and it shouldn't come up further than the shoulders ^^
Also, be careful incase it gets so relaxed and falls asleep in the water...We all know how they sleep so deeply, they could easily drown.
Hope it helps~