The discussion here is more of less for all fans of Gate to enjoy how the events of the Gate will impact in the Marvel Universe rather than invading the original setting. You could role play or put a spin on how this change will effect even more.
Phase 1: The Invasion on Manhattan It was just another warm sunny day in New York. The civilians there were just casually minding their own business, either driving their fancy cars or having a stroll with friends. Despite 'recent events', it wasn't going to stop them to have a wonderful time in the Big Apple.
Just when things continued to be normal, a massive structure appeared in Times Square. The locals, curious slowly approached the structure only to find something worse. Exiting out of the structure were a blend of men and monsters. With one roar, the city went into panic.
An army poured into Manhattan, slaughtering or capturing anyone in their wake. It wasn't long for the police to arrive but they were barely holding this unknown enemy. Just when it seems everything was about to get worse, a familiar set of webs caught the weapon wielded hands of the soldiers.
"Woah there! Didn't mommy taught you that you shouldn't run around with sharp objects?"
It was the one, the only friendly neighborhood Spider-Man. Our web slinger took immediate action after wrapping up a squad of these soldiers. Swinging towards the streets, Spider Man fired webs into faces of the soldiers with one of them shouting his comrades to destroy the pest.
While Spider Man could slip away from the ground forces, he wasn't ready for the air forces. Thankfully, he wasn't alone. Beams and lightning from the sky decimated many dragons. Arriving were the Thor and Iron Man.
Iron-Man asked "Anyone explain to me why Times Square has become something out of Peter Jackson?"
Spider-Man immediately filled them in, "Long story short, the city's under attacked by an army of Romans, trolls, ogres, pig men, beastmen and dragons and it all has something to do with that portal in Times Square."
"That's all I needed to hear. Not to worry, this isn't my first time in a Mid eval festival. All we need to do is to put the apple in the mouth."
One by one, heroes of New York emerged to counter the threat. Captain America lead a charge, Hulk smashed through the opposition, Punisher delivers vengeance on behalf of the souls that were lost and many more.
The Empire who initially had the upper hand was losing ground every second that passed. They hadn't these many Apostles before. What did they charged into?
Suddenly, a shadow enveloped them. They looked up and saw a massive creature unleashing what could be God's wrath and unleashing metal dragons and metal men from its body.
Inside the flying 'giant', an agent informed his superior.
"Director Fury, our forces are engaging the enemy. So far, they couldn't put a dent on us." said Agent Coulson.
"Make sure it stays that way and get me the Avengers."
The Empire pulled back. The enemy was stronger than they anticipated. However getting back was the most difficult they ever faced thanks to a certain God of Thunder who demanded they stand down. They did without complaints.
Anyway, that was my take on if Gate crossover to the Marvel Universe. Please do enjoy your time and make stories of your own here.