There are many mosquito species that don't eat blood at all, for example the elephant mosquito. Blood feeding evolved as a strategy in some mosquito species as an efficient way for females to get nutrients (protein and iron) which they use to produce their eggs (male mosquitoes don't suck blood in any species). It is possible that removing one species might open up the niche for another, however I think it is generally unlikely that a non blood-feeding mosquito would become blood feeding because they are already suited to a niche. Perhaps given enough time (on an evolutionary scale) it could happen.