Are we talking about Neolamprologus brichardi here? There are of course other "brichardi" cichlids: Tropheus brichardi and Chalinochromis brichardi for a start, perhaps others.
In any case, no, you cannot keep Malawian or Tanganyikan cichlids in a brackish water aquarium. While I've heard of this being done by some, there does seem to be a correlation between the use of salt and something called Malawi Bloat. Quite why salt causes special problems for these particular hard water cichlids, whereas it seems to do little harm to a great many Levantine and Central American cichlids that also come from hard water habitats, I cannot say.