It would depend on ground speed. If it had lift from a headwind and was flying forward very slowly (ground speed say 1-2mph), maybe friction could grab it. Otherwise, only if it dives in vertically - At 100mph (ground speed), momentum will cause it to lose traction with the treadmill and skip for a distance until momentum is scrubbed off. The frictional force is the same thing that the treadmill lacks on a plane with wheels. At 100 mph ground speed, if you managed to create enough friction to capture the glider fuselage, momentum would probably rip off the wings. For proof, look at the historical pictures of the WWII gliders in Europe.

In the case of the airplane on the treadmill, the treadmill can't build or counteract momentum of the airplane, because the tangential force applied in a horizontal direction to the wheels cannot be transferred efficiently.... because (unlike the glider), the wheels spin. If from a dead stop, the plane's wheel bearings were completely frictionless, I doubt there would even be much inertial movement of the plane with the engine off if you spun the treadmill at 500mph - because to overcome the resistance of the air surrounding the plane, it would require more power transfer than the treadmill was able to provide. However, once the plane's engine is on, the plane CAN build momentum and speed, since it has a prop or turbine that can bite and move air to create thrust.

Have you ever seen an "on-car" dynamic tire balancer work - you know the one where you jack up the car at the corner and the machine spins the wheel up to 50 mph? Have you ever seen a car thrown off the jack from wheel spin generated by the machine?

Frank