You will find some people swear by feeding nems with pieces of shrimp and silversides. Others say its a big no no. Either way I think moderation is the key.
Overfeeding, specifically larger pieces, can cause the food to sit to long while being digested and start to decay. Other than that, one negative is that it makes for more nutrients in the system. I don't know how much I really buy the "food decaying in their stomach" argument but it's a pretty common one. I've seen several different species of anemone spit food back out after they've "swallowed" it so I don't see why they wouldn't just do that.