A vote for "No" with some input from my aerospace engineer dad. I'm also in the industry but as a tech writer (i.e. no real knowledge). Here's my experiment...
Take an average Hot Wheels car. I like the ones made of shiny gold best. Put it on a regular treadmill at the gym. Turn the treadmill on. What happens? The car flys off the back.
Go retrieve the car. I'll wait. Got it? Good. Now place it on the treadmill and have a friend turn on the treadmill again. The car again head backwards on the treadmill thanks to our good friend Mr. Friction. However, this time something I like to call "The Hand of God" (your hand) steps in and holds the car in place. The car is now stationary on the treadmill. You are exerting a force on the car, albeit a very, very (nearly undetectable) small one as the car is very, very tiny.
Now exert a bit more force (without increasing the treadmill's speed)...the car moves forward on the treadmill. If your friend increases the speed of the treadmill, at some point forward progress will again halt when the speed on the car produced by the force (your hand/arm/stregth) equals the speed of the treadmill.
Now lets head outside where John Travolta has kindly donated his jumbo jet and an extra large mile and a half long treadmill (just to be safe) for this experiment. We start the same way, but firing up the treadmill with an unpowered plane. Wham the plane flys back and off into the distance.
It's gone, but thankfully we have another ready to use. We fire up the treadmill and the plane again drifts back. But then we use the plane's own "Hand of God" (the big jet engines) to match the speed of the plane to the speed of the treadmill. Again, like your hand holding the car in place the plane's engines (much bigger hands for a much bigger objects) keep the plane from moving. The engines are roaring, but because no air is moving over or under the plane's wings, everyone's grounded.
Also think about it this way:
You're driving a plane down a runway at a constant 50mph. The second half of the runway is a treadmill spinning at a contant 50mph. What happens when the plane reaches the treadmill? I think it will stop and would invite other points of view.
This topic has completely ruined my day and my run. My girlfriend hates me because all I've been talking about is finding a surplus 747 and 2000 treadmills.