As far as the Catholic church is concerned, the answer is yes, provided they have the proper "intent". The proper intent is to intend to do what the Church does, that is, to administer Trinitarian Christian baptism.
Remember, the spiritual effects of a sacrament come from Christ, not from the minister of the sacrament, who is just an agent or intermediary. Neither does it come through the faith of the minister.
However, this gets tricky if the minister is, e.g., a Mormon or JW. Those sects use the correct words, but do not mean by them what the Church means (because they reject the Trinity), so they are assumed not to have the proper intent.
However, if someone were baptized by a Mormon, and had a signed letter from the Mormon indicating that he or she intended to administer orthodox Christian, Trinitarian baptism, I think it would hard to argue that that baptism was not valid.
I did not know this was a Caucus thread, but I asked a legitimate question and I got legitimate answers.
Thank you all!