Do pilots adjust the aircraft's flight path to allow for the curvature of the Earth?
Aircraft altitude is measured (inferred) by atmospheric pressure. The aircraft is usually flown at an altitude that maintains constant ambient pressure (by pilot or autopilot, as the case may be). Changes in local barometric pressure (provided by air traffic control) are used to recalibrate the aircraft altimeter.  As long as the aircraft is flown at a constant ambient pressure (hence constant altitude), it will be following the earth's curvature (as the atmosphere is attached to the spherical earth and has same properties at same distance from the center, in an ideal case) as the altitude is measured from the surface, which is curved, and not a plane.