The problem is that the term Easter Egger doesn't really mean much. EE's are not a breed, there are no standards for them. It is just a name for a chicken that might or might not have the blue egg shell gene. Since a rooster does not lay an egg you can't tell if he has it or not. That changes if you know what breeds his parents were. What do you know about his parents? Were they any specific breeds? But without specific information on his parents you just don't know.
That goes for what color eggs his daughters might lay and what color/pattern the chicks might have.
I don't see any barring on him, so with a Cuckoo Marans mother any boys will be barred and any girls will not be barred. That's half-way to making black sex linked chicks. The other part is that the boys would have a spot on the head where the girls would not. Would you be able to see that spot in the down when they hatch? I don't know enough about his genetics to be able to answer that for sure, but I think there would be a pretty good chance. There is a real good chance the chicks will be black or mostly black because of the mother's genetics.
Then you have the question of how dark an egg does that Marans lay? The darker the egg the better, but some just don't lay eggs that dark.
If he has two copies of the blue egg gene, then he will give one to all his daughters and all her eggs will be blue or green. If he has one blue shell gene and one not-blue, then abut half his daughters will lay blue or green eggs and the others will lay brown. If he does not have any, then all the daughters will lay brown eggs, no blue or green with that hen.
If that Cuckoo Marans hen is a good egg layer and the rooster's mother and grandmothers were good egg layers, the pullets probably will be too. You can see how well that Marans is doing but he does not lay eggs so you don't know what genetics he is contributing to egg laying.
There is only one way to find out, try it.