When flying straight and level, with the airframe set up for cruise (eg. no flaps, gear up, etc): yes. Weather conditions don't matter; the plane's speed throug

When flying straight and level, with the airframe set up for cruise (eg. no flaps, gear up, etc): yes. Weather conditions don't matter; the plane's speed through the air will remain the same, and it is the airspeed that matters when it comes to keeping the plane flying. Windshear can temporarily change the airspeed due to inertia, but keep the same power setting and the plane will catch up by itself. When doing anything else, such as climbing, descending, etc: the required power settings will be different, but can be predetermined. Turning will reduce airspeed for a given power setting, but if the fault is known, the turn can be done with a small enough angle of bank that it won't matter. This can be done by the pilot, or for the sake of this line of argument, a computer could easily be programmed to limit the bank angle when an airspeed indication is known to be unavailable.