Unless the EE carries Silver, this is unlikely; the genetics of Easter Eggers are nearly impossible to determine as they are mutts. I've never seen one which carried Silver. So the chances of producing a sex link are low.
The offspring's egg color depends on what the mother is carrying. If she is a homozygote for the blue egg gene (O/O) and produces a blue egg, all of her offspring with a brown laying cock will produce green egg laying offspring. If she is heterozygous (O/o) and lays a green egg, then only fifty percent of the offspring will produce a green egg and the other 50% a brown.
