They are non-obligate egg feeders, but a lot of people find the neonates to be fragile. They seem to like film canisters placed on the ground and tilted to be mostly horizontal (like a cave). That also makes it easier to collect eggs. If this your first dart, I'd highly suggest something more like tincs, leucs, or auratus. Retics are a lot more touchy than those, and can squeeze out of very tiny spaces.
If you leave the eggs in, the parents should raise them up just fine. They froglets will be smaller than if you do it yourself. You can raise them on the ole' algae recipe. But then again, I personally have never raised reticulatus tads. Good luck with that.