I believe most folks that raise brine shrimp do it separately from their main tank. However, brine shrimp are not the most nutritious things in the world. Many LPS
corals will eat meaty foods, chopped up finely. I normally feed mine mysis shrimp (not brine), cyclopeeze, and some zooplan powder a couple times a week. Many folks don't target feed their corals at all. There are some though - sun corals, for example (which may be your "yellow colony polyp"... not sure) - that are not photosynthetic and will NEED to be feed to stay alive.