She's likely to have the gene, yes.
The differentiations that people make when it comes to "show" eggs - like the difference between blue and greenish blue - are not an an indication of a different gene. It's not like there's a blue egg gene and a green egg gene. It's just blue. Blue plus various tinting from the normal colors a hen paints on her eggs makes the shades of blue and greenish blue and light green and olive that come from EEs. But if you showed a poultry geneticist an EE egg he's not going to say "Oh, that's different from this Ameraucana egg."
I personally think the reason people get "pink" from the birds with one EE parent that don't have the muffs and comb and leg color is because normal EE - that light greenish blue - is blue plus the tinted light brown that people tend to call pink if it comes from EE parents and call tinted brown if it comes from a Wyandotte. EEs "must" have some different color, so when they lay a tinted brown egg it gets called pink. But if the bird had either one or two blue-egg genes it would be greenish blue.
As has been pointed out very ably, the gamey little bearded birds we call EEs are the true originals; somebody took a few of them and decided to concentrate on a few colors and a single egg shade and call them Ameraucanas, but EEs qualify as a breed or landrace just as well as any other. It honestly makes me smile when people say that they're "mutts that inherited the blue egg gene" - they're "mutts that inherited the blue egg gene, the beared/muffed gene, the skin color gene, the body type genes, and are very predictable in color and they breed true." Last time I checked, that's pretty much all ANY of the breeds can say. So the greenish-blue typical EE egg is nothing to be ashamed of.