Eh. We already had at least one of those NOTAMs near us in Southern Indiana a few weeks back. I flew during it, the GPS worked fine. If it hadn't, there's the VOR radio navigation, if that doesn't work, there's a compass and a watch, and the fallback of landmarks. The first two methods would work for airlines, the last might be a bit tricky for them to pull off from 30,000 ft.
The plane that is recommended to avoid the area has a GPS-only derived AHRS (Attitude Heading Reference System), which replaces the instruments that tell a pilot what straight and level is and which direction the plane is pointing. Pretty important when you're in a cloud.