If you get cories and they feel threatened by any fish in your tank, they will hide and you may never see them. You will also have to get at least 3 of the same species (better to have more) so they can shoal together. I'm not sure about all species but julii and trilineatus corydoras let off a toxin when they are attacked or stressed. So if a fish gets a hold of one, the toxin will kill the attacker. In a tank, the toxin is diluted, but it will kill any fish that are in bags with the cories. If you get cories and say neons, have the LFS put them in separate bags!
I'm not an expert on cichlids, but cories aren't very aggressive fish and are very peaceful. While they can be fast at times, its usually not over an extended period. Are you cichlids more mellow? If they are, you may not have problems, but I would be worried. I wouldn't want to risk losing a couple cories or a cichlid. I would suggest maybe a faster fish? I have two great danios in with a severum and they do excellent together. When I first put them in the tank the severum tested them, but they flipped out and sped off to the other side of the tank. Now the severum won't go near them so the danios dominate most of the tank. I think the neons (though they are small) are pretty fast and as long as they can out swim the cichlids, they will be fine.