Officers did indeed wear squadron numbers on the left sleeve, although it was not common place. In "World War I German Aviators, The Sanke Cards" by Charles Woolley, there are at least two period cards of officer aviators that clearly show these oval numbered patches up close in studio portraits.
On page 139, Offizierstellvertreter (An NCO with temporary officer rank) Fritz Kosmahl wears one with '22' on it.
On page 235, Leutnant Emil Thuy wears one with '53'.
On Gary's tunic, I tend to lean more toward the outline being that of a machine gun badge. The aviation squadron ovals are elongated vertically, whereas the machine gun badge was more horizontally ovular. If my eyes do not deceive me, I do believe I can see the ghost images of the body of a machine gun as well as the legs.