At the character breakfast buffet at Cape May we asked our server about Egg Beaters and she had someone in the kitchen whip up Egg Beater omelets for us.
As the PP mentioned, Boma has an "eggs made to order" station at the breakfast buffet and they definitely have Egg Beaters (or equivalent) on hand.
So I'll go out on a limb here and say that I expect any WDW restaurant that serves eggs at breakfast would also have egg beaters on hand. Just ask your server.