Problems with the cockatoo is that the corys and cockatoo are both bottom dwelling fish which could cause fighting. Corys usually come out on losing end of fights, because they usually won't defend themselves against an assault, rather choosing to try to run.
The rams tend to be sensitive to nitrate waste products, in my experience. That would mean that you would HAVE to be very diligent with waterchanges and be very careful about the level of bioload amongst your tank's livestock to avoid chemical levels that may become problematic for the rams.
