Channel cats will eat anything that fits in their mouth. So, yes they will eat the minnow population down considerably. My pond had FHM's and crawdads stocked for a year before anything else. My gamefish population suffered some the first few years due to them washing down the drain pipe (I think), but the FHM population went from millions (maybe) to the occasional one in the crawdad trap in only two full seasons with the HBG and HSB. They are easy pickings and made great weight gains for the lower population of gamefish, however.

Gold fish have a bad reputation in ponds that are desired to be a fishery and not necessarily a goldfish pond. They tend to overpopulate and muddy the waters up more so than others that tend to do the same. Small goldfish in ponds get to be big goldfish, big enough that the predators can't eat them, then they make a lot more goldfish. A bad idea IMO. A good read by Helen Palmer Geisel - "A Fish out of Water", lol, circa 1961. A children's book from my memory...thanks for the flashback!

Carp are very good to eat IMO, but unless your pond has plenty of established plant life, they may take a while to grow. Although feeding them would not be hard to do. I think you may be onto something with carp and FHM, but I'll rely on a more experienced PB member to reply on that idea.