Ya, if there's some kind of clorine type substance involved, it could eat through the wool, or so I have read.

I looked over a chapter on dying fabric in a costoom tech book to see what would be involved with dying the whole kilt. I guess it might be possible, but I'm not sure it's practical if for no other reason than you would need a really big container to get an even dying without adjetating the wool.

I know others know much more than me on this subject.