True. I'm not really talking about the Predators themselves though. The first AVP film is quite evocative of certain elements found in At the Mountains of Madness.
OK, stay with me now, this is complicated.
Dan O'Bannon and John Carpenter are both massive fans of Lovecraft, and, after working together on "Dark Star", went on to create their own Lovecraft-inspired works. Carpenter created "The Thing", which was a remake of Howard Hawks's "The Thing From Another World", which was based on John W Campell's "Who Goes There?", which was "inspired" by "At the Mountains of Madness". Carpenter's remake, however, reintroduced many Lovecraftian elements into the story, connecting it more closely with its inspiration.
Dan O'Bannon went on to create "Alien", whose original script was far more closely tied to "At the Mountains of Madness" than the final product. In the original story, the planet was once home to a primitive civilization that worshiped the Aliens as gods, and the eggs were found in a sacrificial chamber inside a pyramid. Just as in "At the Mountains of Madness", much of the now extinct race's history is gleaned from reading hieroglyphs on the walls. Giger even created images of the hieroglyphs and the pyramid, but the concept was scrapped, most likely for budget reasons. Giger himself was very closely tied to Lovecraft, and his original design for the Alien was based on a painting he did called "Necronom IV". No doubt their mutual love of Lovecraft is what connected Giger and O'Bannon when they met on the set of Jodorowsky's abandoned "Dune" project.
While the concept of the primitive civilization worshiping the Aliens as gods was dropped in the original "Alien", it was reused in "Alien vs Predator" which, coming full circle, was set in Antarctica. So. I hope that clears things up.