The short answer is no, 99% of UberX drivers will not be able to pick you up at the airport. Some of the taxi cab companies here are running an UberX/taxi cab company hybrid here where they give you a Prius to drive UberX with and you cut them in on 50% of your revenue, and they can pick up at the airport, I do believe.

Apparently, Lyft drivers shouldn't be able to pick up at the airport, but their app still allows them to do so, illegally. On the Uber app, it won't even allow normal UberX drivers to pick up pings at the airport. Of course, Uber drivers can always drop off at the airport. The ability to pick up at the airport is based on a contract, and only x number of cars are allowed per the contract, and I believe the only two companies than are permitted to pick up is Green Air and Yellow.

Source: I drive UberX in Phoenix as a side job.