Don't quote my opinion as authoritative, but I've soaked hairpieces in Pure for like three days (in order to get glue and the like out of the hair) without any noticeable damage to the unit, other than perhaps a little lightening of the hair dye. But I have to re-dye the units every now and then anyway, so this wasn't a major issue.

P.S. For such touch-up dyeing, I've taken to just dyeing the unit while it's on my head with a hair dye brush.