Sort of... When an airplane flies overhead, between you and the sun, it will block out the sun, or a portion of it, depending on the airplane's size and altitude. That is the airplane's shadow.
When light strikes an object, the air molecules in the atmosphere bend and disperse the light around the object. That dispersion makes the shadow less defined the further away the object is from the surface.
You can see this if you pick up a ping pong ball from the ground at noon on a sunny day. Sitting on the ground, the ball casts a well defined shadow. As you lift the ball from the ground, the shadow becomes less and less distinct due to the diffusion of the light, to the point that it all but disappears at some height.
An airplane is the same... as the airplane climbs, its shadow "exists", but is so diffused that it may not be noticeable, and in any event is too far from the airplane to be seen from it.