I got a Beautiful Bhrama hen from a friend & it's grimey & full of old used cookin' oil & dirt...she's only 'bout 7 weeks old, & will molt her feathers, but she's disgustingly ugly in the condition she is in...
Yeah, if she's gross I'd give her a bath! I gave my silkie mix a bath using some dog shampoo when she got all gross, and it did wonders! She looked like a while new bird. It's actually kind of fun bathing chickens, haha. Go for it!
I had some chicks that used to sit under the ducks face when he ate, and boy did he slop the food about! lol They were covered! I gave them baths, some of them really liked it. Just make sure you blow dry after so it doesn't get chilled.