Angel fish will generally be more competitive than discus when it comes to feeding, territory, etc. In my experience, I've kept discus and angels together, but never for a long time. Discus have a tendency to establish pecking order based upon the size of the fish and fins; angelfish tend to have bigger fins relative to their body size. As a result, even if you have smaller angelfish in the tank, their fin factor will deter the discus from being aggressive towards them. In my experience, it's better to have large dominate discus and small submissive angels, but this simply doesn't stay the case for too long. As far as diseases go, yes angels have greater immunity to diseases, but if the fish are healthy and happy, the water parameters in check, and fed regularly, disease transfers will be rare and generally not severe. If and when my discus get ick, bruises, or scarring, I just do a water change and feed live food. Aggression is directly proportional to food scarcity; by increasing the amount of food I feed, aggression (and therefore the cortisol level) is reduced and the natural immune response can be maximized. I say give it a try, but be ready to transfer the angels to another tank if necessary.
Good Luck!
-NF