Yes. Some (not all species) female mosquitoes drink blood for the protein, which they need for egg production. Their actual diet is nectar from flowers.
I mean, I hate mosquitoes as much as the next guy, but that sounds like a great way to destroy whole ecosystems that rely on mosquitoes as a food source.
But keep in mind there are a lot of invasive populations of mosquitoes and some of them are disease carrying species. Since they're invasive, by definition they're not vital to the natural ecosystem and those populations could be safely wiped out.