I almost never see my babies eat--I can only tell they eat because I find their little poops.
I don't think a vet visit is warranted. What exactly could a vet do for a hatchling? I think they are too small and fragile to treat. If you supply them with the right environment and the right food, I think it is pretty much up to a hatchling whether it lives or dies. I doubt any vet could make a difference. Hatchling deaths are either from some problem they are dealing with since before hatch or poor husbandry, neither of which are in the vet's control.
I am a little concerned you say you have seen your hatchling drink. Are you keeping the enclosure humid enough and providing enough misting? They are very fragile at this age and it is very easy for them to dehydrate.
I don't skimp on the food I put in baby cages, especially since I don't have as much experience as some of the other breeders commenting here.