The US is more likely to actually accomplish something when election meddling unlike other who are just hacking the systems to mess with US intelligence. China would be the one exception since they probably have the most vested interest in the US since they own around 5% of US debt, but since they need the US dollar to be stable any of their meddling is going to be keeping the status quo in power. Putin also wouldn't try to radically change the US government with actual election meddling, he's too cunning for that and his ex-KGB past would have him being more covert.
No country that I'm aware of has actually been able pull off any large scale meddling in US elections. While our system isn't perfect, the Electoral College makes it tougher for a foreign country to actually be successful because it would require a massive scale of meddling (even the US couldn't achieve the necessary scale). I sorry just don't see your scenario as plausible since many of the legitimate humanitarian assistance NGOs try to stay out of politics, it hurts their donor levels when they enter that realm. Your argument reminds me of the argument against letting Irish Catholics (really all Catholics) in because the nativists were afraid the Pope would try to take over the US.
If people want to come then the government should say "ok but no handouts from us" just as they did before Welfare, Social Security, and Medicare existed.
Sounds like a good way to let foreign countries financially promote mass immigration to cause large swings in voting bases in a different country. Almost like election meddling.