I'm not real good at egg color genetics but from what I understand there are several different genes that affect the final egg color. I'm not sure which are dominant. A lot of Easter Eggers have mixed genetics too, so that makes it even harder.
I've heard that all egg shells are basically blue or white to start with, then some hens add a brown coloring on top of that basic egg shell color to give a final color. There are a lot of differences in that brown, from a pale creamy color to the chocolate brown of a good Maran. So if you start with a blue base color and add:
No brown - you get a blue egg
Light brown - you get a green egg
Dark brown - you get an olive green color
If you start with a white base color and add:
No brown - you get a white egg
Light brown - you get a light brown egg
Dark brown - you get a dark brown egg.
I've paid attention to the inside egg shell color after removing that membrane. My green eggs are really blue underneath. My brown eggs are white inside, but the actual shade of white seems to vary a lot. Some of that white underneath I'd really call cream colored or light brown. My darker brown eggs are almost a pure white underneath though, not creamy colored at all.
Not much help, I know, but especially with possible mixed genetics on the EE rooster, I'm not sure there is a clear answer. I think you can only try it and that you will probably get some blue or green eggs. Maybe if the rooster is pure for blue eggs you can get a guarantee of either blue or green eggs.