I don't want to sound alarmist and I am obviously not an expert but... we know what happens when you remove a species from the food chain.
The Culex quinquefasciatus (from Google's EPA request) is not native to N. America, it likely originated in Africa and came across due to human activity.
There are over 200 species of mosquito in N. America (worldwide about 3500). Taking one out will have negligible effect on the food chain.
Bats, specifically, will eat mosquitos but prefer larger insects. Mosquitos are small relative to the effort the bat takes to catch therm.
The specific mosquito mentioned is available in lots of places around the world (not native - see first point above), so we could repopulate if we notice a problem.
Google is breeding these mosquitos, so we have breeding populations and we could repopulate if needed.
It's the primary vector for West Nile virus, St. Louis encephalitis virus, Avian malaria, and Wuchereria bancrofti (a parasitic worm).
I've been following the progress of these sorts of activities for many years. With proper care and monitoring, it's possible we could fix a lot of invasive species problem such as Cane Toads in Australia, Mongooses (mongeese?) in Hawaii, and Aedes aegypti. A. aegypti strongly prefers to bite humans and is carrier to disease, and is also not native to N. America.
The US used to have screw worms. The screw worm would lay eggs in an open wound on mammals (usually domestic animals such as livestock, but sometimes humans) and the larvae would develop under the skin by eating healthy tissue.
The US government began a program of releasing irradiated screw worm males, which are sterile, into the environment to compete with healthy males. This reduced the population, eventually down to zero, and now the US is largely screw worm free. This only took about 10 years.
Good riddance.
Now do ticks.
The full explanation is Sterile Insect Technique.