Yes, there's a very good chance that your EE will lay colored eggs. On rare occasion, they do end up laying pink or brown eggs, but that's not as common as blue/green. I'm not an expert by any standards, but I'm guessing the reason for this is that they're mixes?
EEs are basically, like I said, mixes with some or a little Ameraucana blood in there. The true Ameraucana has different traits than an EE, such as specific color varieties like Blue, Black, Splash, Wheaten, Blue Wheaten, ect. (whereas with EEs, there's no telling what color they'll feather out), they're fluffier, I believe their legs are slate rather than willow green, and their skin is white. Plus, true Ameraucanas are very hard to find and are quite expensive. I've got both, actually, so maybe I can show you the differences.
Here are some of the EEs I've had/still have:
And a few true Ameraucanas:
Sorry, the Blue girl has crossbeak.