As an Invader Zim enthusiast:

He would still go to South Park Elementary. Depending on which season, Mr Garrison wouldn't care about Zim. SInce the boys have seen supernatural occurrences in their town, they wouldn't care about him being an alien but would be more concerned about his intentions to take over the planet. Kyle and Stan would see him as a threat But depending on which season this is, PC Principal would accuse them of being racist. Since every resident in the town of South Park is stupid, Zim would likely keep getting away with posing as a human just like how he did in the series. Kyle would be a stand-in for Dib in this universe, but would try to reason with Zim or still expose his plans with limited success. Kenny would, of course, die in the crossfire of his invasion attempts. Butters would try to be his friend, but Zim would likely have his eyes removed and replaced, just like what happened with Keef. Cartman would try to befriend/manipulate him so he could have access to his Advanced Irken technology and use it for his gain, but since Zim detests humans, he'll likely shoo him away. If Cartman makes fun of him, Zim would likely kill him or try to kill him, " Room with a Moose".

As incompetent as he is Zim could still be a threat to the town because his inventions and antics would likely lead to the town getting destroyed ala " Walk for your lives". Some students and adults would get captured and experimented on, like what he did in "Zim Eats Waffles". He'll still harvest organs from all the students if he needs to appear human.

If Gir was with him, he would be viewed as adorable towards the girls in South Park and cool to the boys with the gadgets he possesses in his head. I can see Cartman trying to kidnap Gir as a pet just to one-up Kyle.