It did and the (
redacted) cat loved it!
Once it was feeling mellow and not acting like a chainsaw we gave it a bath with the same flea shampoo we use on the dogs and the occasional chickens we take in. The chickens we take in often have chicken lice and mites and a bath in flea dip takes care of that. At this point it's just a rule that new chickens get a bath.
The cats usually don't need a bath but this one was ill and it wasn't going to get any better until the ticks and fleas were gone. It lived with us like four or five years and then disappeared one time. No idea what happened to it.