While it's presumptuous to think just any pop culture phenomenon will endure a thousand years, Earth's Mightiest heroes seem to be more tailor made for the world of Medieval America than most. Many characters like Captain America, Black Widow and Hawkeye almost seem tailor-made for an adventuring party. Captain America's mix of chainmail and star spangles makes him a very "If he didn't exist we'd have to invent him" figure. And of course, the presence of Thor, and honest-to-God figure from actual medieval times to legitimize it. The first Avengers movie almost goes out of its way to evoke dragons, ogres and the Mouth of Sauron. I'm not the biggest fan of "scientist=wizard", but they definitely made it easy.
But even if it's not the same exact lineup (The team roster from the comic changes over the years), it definitely left an indelible effect, not just on America, but the world. Just about every country has its own version of The Avengers, even if altered to accommodate its own regional culture.
The lineup we're most familiar with is probably mostly located in the Non-Denominational world, as Captain America definitely comes across the most as a sort of American Roland figure. As we move away, fidelity to the United States as a concept would fade. In fact, the Cowboys would not be big on the knights of the forest zone, and less likely to appreciate pagan figures like Thor. This would see a huge break in the "classic" Avengers. As we go out west, we would see Captain America altered to resemble the country faith of New Mexico, California or the Pacific Northwest, possibly merged with Iron Man. Thor may be replaced with Thunder Gods from Indigenous or East Asian cultures, less influenced by Europe. Other Marvel heroes like Spider-Man or the Human Torch, or wholly new creations to fill in the gaps, but the core usually consists of an armored/shield-bearing hero, a female warrior, a monster, an archer and a Thunder God.