Don't know enough about the Hays Code to say but the effect of no comics code would be huge assuming they do something more sensible like just introduce a ratings system and don't put super graphic stuff on the covers like they did OTL.
The first and biggest would be that EC comics would not shut down meaning there's always going to be another huge company to compete with DC from day one. The biggest point is that, of course, EC didn't focus on super heroes (though the would probably create there own to compete with Superman, Batman et all). Horror was it's stock and trade but it had every genre. Without the code preventing these comics from being made superheroes wouldn't dominate the medium nearly as much, leading to a much greater diversity in content in comics that might lessen the perception there "for kids". Another knock on is that DC wouldn't become as complacent in their stuff. There early monopoly caused the company to stagnate creatively that lead to the creation and rise of Marvel, but competing with another company that's as large would mitigate that.
The silver age is considerably different. Without the code the comics wouldn't be as wacky and aimed at kids, and would probably come to resemble the later stuff down in the late 60's early 70's much faster.
Hard to say if Marvel still comes around. The company that preceded it still exists of course but it's impossible to say if people like Stan Lee and Jack Kirby would all be working there with another company in the game. Granted someone is bound to pick up Stan and Jack eventually, there to talented to ignore.
Huge butterflies all around basically.