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No. You'll just get EE green eggs.
Olive Eggers and true olive eggs come from a DARK brown layer x blue or green layer.
As to the EE x white egg question, yes, granted the EE has the genes for blue, not green.
I've got an Easter Egger mutt that is part Polish, part EE. She lays light blue eggs.
I once had half Black Copper Marans, half New Hampshires - Laid pumpkin paste orange eggs.
I have various Olive Eggers - not laying yet but expecting different shades of dark olive.
I have some EE's from different breedings too, not laying yet but expecting different shades of a normal EE green.
I have some Black Copper Marans x Polish, expecting light brown or speckled eggs, but they're too young to even wait for eggs. They're just about 2 months old, still time. . .
At this moment, Olive, super-dark Plive, and Slate Gray are the only egg colors I don't have. Otherwise, I've got blue, robin's egg blue, light blue, shiny green, matte light green, pink, brown, speckled brown, pumpkin-orange, dark red, purple, and white.