EE's can lay brown eggs just as well as green or blueish. The only specification of easter eggers is that they have the colored egg gene. Plus, we have to remember that EE's are a "mix" in the first place. However, if she lays green/blue eggs then yes, you're correct, she is an easter egger.
There are two camps on the EE and eggs other than blue/green thing - the camp that throws everything with blue gened parentage into the EE camp regardless of the color eggs the bird itself produces, and those that put only those laying colored eggs in the EE camp, other birds with mixed parentage which happens to involve blue egg genetics into the "mixed breed" category.