I think Marvel and DC would absolutely exist; they would just be far less popular since they're selling a "fake" version of something people can get every day. I also don't think in-universe comics of this world's contemporary heroes would be terribly popular, either, since they're guilty of the same thing. If I'm an Icon fanboy, maybe I want to read Icon comics, but if I'm just an average Joe who loves Icon then I only care about his real adventures. Comics based on real world heroes probably feel trite and cash-grabby to most people.
EDIT: However, comics of Lady Liberty's WWII adventures? Those I could see being popular, since so much time has passed and those adventures have ascended to legend status.