It depends on the specimens of pearl gourami and of BA tetras, the number of BA tetras, and the order of events.
If the tetras are still small, and the pearl gourami coming anew is a larguish male, it could be okay.
But I would not introduce anew a pearl gourami into a tank already containing an established group of full grown BA tetras. They are not terribly nippy, but nippy they are, and they act as a pack. Good luck!