I am not 100% sure about killing all the mosquitoes (even if its just the Aedes aegypti). After all we are in an ecosystem, and mosquitoes plays a major food sources to other animals. Not to mention their ecological role as a vector for diseases, that keeps us and animals populations negatively regulated
Aedis aegypti is invasive at least in the US, so that shouldn't be a problem. But generally, one should be careful, yes.