They do, but because of the shells on the eggs I am not sure, and I do not know of their nutrition content but chicks would be in the eggs are chicks are incredibly fatty.
Egg eating snakes have teeth in their neck that are attached to their spine. These are used to crack the egg and the shell is spat out. Corns dont have these. However, I have heard of other rat snakes eating eggs (that also dont have these teeth) and I have seen few pics. So they probably can, but I wouldnt.
Remember they dont need "treats". If you want to give them something to do just change the viv design.