EE's are not a breed. They are just chickens that could have the blue egg gene. Could, not necessarily absolutely do. There are no tendencies or standards for them, color, size, pattern, traits, anything.
There are no tendencies for EE's to lay early. There are no tendencies for EE's to lay late.
Egg color depends on genetics. If the hen has even one copy of the blue egg gene, she will lay a blue or green egg. But if she only has one copy of that blue egg gene, you don't know if her children will inherit a copy of the blue egg gene or not. Same with the roosters. EE's are mixed breed chickens. You really don't know what their genetic background is.
There is a possible link between the pea comb and the blue egg gene. Those genes are very close together on the chromosome. In almost all cases the pea comb and blue egg gene will travel together, but that is almost all cases, not quite all. It is possible that they can be split and a hen with the pea comb will not lay a blue or green egg or she will lay a blue egg and not have the pea comb. So, yes, the pea comb is a good indication that they might lay a blue or green egg, but it is no guarantee.
I can complicate that a bit further. When the chicken has only one copy of the pea comb, the comb will probably not be a true pea comb but can be a wonky looking comb that is somewhere between a pea comb or a single comb. Or if the rose comb gene is present, it can look like a walnut comb. And there are other possible comb modifiers than can make the pea, rose, or walnut look funny too, like getting a buttercup comb.
With mixed genetics, and EE's are of mixed genetics, there is no guarantee of what you will get.
This article from the Ameraucanas Breeders Association shows what is required for a chicken to be an EE. You can clearly see there are no requirements.
Where a lot of confusion comes in, several hatcheries sell chicks that they call Ameraucana or Araucana that are really EE's. Many of these flocks are based on Ameraucanas but they have had other breeds mixed with them to get the pretty colors and patterns and to improve egg laying. Some people think EE's should look something like Ameraucanas because many of these flocks were created from Ameraucanas, but that is just not true for EE's in general.
Some people think EE's came from Ameraucanas or Araucanas initially, but that is exactly backwards. Ameraucanas and Aruacanas were created from Blue egg laying chickens that came from Chile. The EE's were here first.
Denverbird, I don't know where you got your EE's, but to specifically answer your questions as simply as I can. EE's in general have no tendencies about laying early or late. That depends on the traits of their parents and those traits can be all over the board. It is also very possible that EE's can lay brown eggs.