I remember reading that the genes that code for a pea comb and green egg laying are located very close together on the chromosome, and tend to travel together during cell division. That's why green egg-layers (and blue egg-layers) tend to also have pea combs. However, I've seen exceptions to that "rule" in my own flock, so who knows? And, pea comb or not, some EEs lay brown or pink eggs. It's probably a fluke that nearly all of mine do lay eggs in shades of green and olive, with a few blues.
When running an EE rooster with our flock, he always threw pullets that laid green eggs no matter what breed the hens were. It was pretty interesting. But he was a hatchery chick, so I don't know what color his egg was.