It's quite aggressive stuff, and can cause problems with some metal objects and especially platings. I've never tried it on brushes, and although the bottle mentions "brushes", I guess it means brushes used in barbering head hair, rather than anything to do with shaving.
Natural fibre shaving brushes (badger etc.) probably wouldn't do too well, and I doubt that synthetics would either. How it might react to the knot glue is a concern. Whilst it's OK for some razors and other non-absorbent items like combs and scissors, I don't see that an absorbent shaving brush, however lightly dipped or well-washed afterwards, will entirely lose all traces of the stuff, at least first time around. I certainly would not want to be applying any Barbicide residues to my face.
The German brushmaker Leonhardy was kind enough to send me a tin of their Pinselseife brush cleaner, which I think is primarily intended for cosmetics brushes. They also make shaving brushes (Rasierpinsel), and seemed to think the cleaner is OK for them. It smells nicely of lemon, is ph-neutral, but I've never used it, or felt a need to try it out. Perhaps I'll give it a try.
However, I think
@Boycie83 has described an excellent regime for brush care.