I've got an emerald dragon and am now waiting for a second one to come. I don't really care for the gems so I wonder whether I should display the second one as egg or hatch it and breed the third one from two previous ones.
No, Emerald Dragons cannot breed, even with each other. From the Dragonvale wiki on the Emerald Dragon:
The Emerald Dragon can ONLY be bred by selecting a Crystal Dragon to mate with a Lichen Dragon at the Breeding Cave/Epic Breeding Island.
Also note that there will be 12 gem dragons, one for each month. I'd recommend keeping the egg as a showcase, as eventually you'll end up with 1 of each gem dragon if you play enough.