Probably! Assuming an infinite universe, anything in the laws of physics is possible, so the bulborb likely could exist. But that's not a terribly interesting answer, is it? A more interesting question - with more interesting associated answer - would be "under what circumstances would a bulborb be LIKELY to evolve?" So I'm going to answer that one too.
First off, you're missing the presence of the Emperor Bulblax, who puts an entirely different spin on things. I propose that, rather than being insectoid, bulborbs are more like our fish. Given their rather bizarre body structure (tiny legs, large body, and eyestalks?), it seems likely that they developed from amphibious creatures, possibly swamp-dwellers - their large bodies are/would be somewhat buoyant, allowing them to maintain a neutral position in the water with their eyes above the surface. Their legs mostly served for limited propulsion, and also allowed them to lunge out of the swamp to seize prey - also a reason for mandibles that can grip quickly. The female and male Bulblaxes are simply alternate forms of the normal bulborb, which are taken for the purpose of mating - the female becomes immensely bloated in order to produce a large quantity of larvae, and the male (her chosen mate) takes on a larger form to protect her, as she is largely immobile while producing young. The male's strange hunting method lets it store food in a crop, which it brings to the female. The general bulborb form evolved during a time in PNF-404's history where there was (for some reason) less heat and light in the atmosphere, possibly due to a volcanic eruption or simply a wobbling of the planet; now that more radiation from the planet's sun reaches the surface, the bulborb swamps have receded, and more durable hides have become useful for staying on land. Their tiny legs are still not well-adapted for long-term action, though, and they are still more sensitive to sunlight thanks to their swamp-protected ancestors, so they sleep during the day to conserve energy and avoid the heat.