Would Americans say 'a three-egg omelette'?

This American would! And I'd cook it in an eight-inch pan. I think it falls under the measurement rule, somehow. Well, the thing that in my head is a measurement rule, like this from Merriam-Webster:

—plural foot used between a number and a noun —plural feet or foot used between a number and an adjective <6 feet tall>

It seems to apply fairly consistently for measurements, so...