Yes. All fish, including the neon tetra themselves, will readily devour any eggs they can find. Getting neon tetra to spawn is not easy. Are you noticing spawning behaviours?
A comment on your loach and cory, they are shoaling fish that must be kept in groups, 5-6 or more, as they are highly social fish. Clown loach get large though, up to a foot, and need a 6-foot tank. Cory are fine in a small group in much smaller tanks. You can read more in our profiles, click on the shaded name to see that fish's profile.