Probably, but it's more a question of how much and how strong they are. As anemones go, BTA stings are pretty weak. Was the entire anemone sliced up, or just a few tentacles?
I once had a post-split RBTA destroy all of his tentacles and oral disc in a Tunze Stream. I removed the remaining anemone base, and siphoned out little bits of rose-colored tentacle tips that were rolling around on the bottom. My skimmer runs wet and there's always carbon in the sump. There were no ill effects in the tank.