I acquired a gander in this state.
He eventually sorted himself out though to be truthful his feathers weren't truly waterproof until he moulted and grew new ones.
I think what happens when they don't have access to clean water is that they preen and preen and use up all their oil.
I watched mine and he was so happy to have clean water, kept washing and preening, that I decided he'd be ok, and so it turned out. Sounds like yours will be too

The only thing I would say is that they get cold when they're like this, since as you say, they do get wet. You just need to adjust for that - somewhere to live with plenty of clean straw will help.