Yes, of course. If I were to bathe one with wet feather I would be very careful and do it only if I thought the bird was stable enough to tolerate getting wet and chilled.
I'm sorry, in the post where I mentioned cat food I was referring to "kitten food", not adult cat foot.
Last time I looked, kitten food was 40% protein and adult cat food is ~30% protein.
Diets in excess of 30% protein can cause helth probems, but either kibble is okay in moderation as treat.