Well, no, it isn't. It's in contact with the ground which isn't the same thing.
Yes it can, as you'll see in a minute...
No, the engines are not connected to the wheels. All any aircraft engine does is move air faster out the back... be it a prop or a jet. All aircraft wheels are unpowered, freewheeling things that stop the paint on the belly of the plane rubbing off on the runway.
So what's turning the wheels then? The treadmill.
True to some extent. If you could actually build a dirty great treadmill and stick a 747 on it, then start up the treadmill, friction and momentum would see the 747 move back along the treadmill, the wheels not turning. However, the thrust from the engines is a separate force and, if the wheels are just freewheeling, it makes no odds how fast the treadmill goes or the wheels spin, the force from the engines will still propel the plane forwards, relative to a point stationary to both the treadmill and the plane.
Again, the wheels aren't powered by anything at all... they turn because of the friction between them and the relative speed of the object they're attached to.
Imagine a landing plane... the wheels aren;t spinning as it comes into touch down but then they spin like fury as the plane lands... that plane could land on ice and the wheels would skid... perhaps even lock up if the pilot applies the breaks... does the plane instantly stop moving? No. That's because the relationship between the wheels and the plane and the wheels and the surface are two different things, which is why the wheels are freespinning...
As someone said earlier, imagine there are no wheels. In fact, how about imagining you've got the worlds first flying hovercraft... the speed of the wheels over the treamill and the speed of the treadmill are unaffected by the thrust of the engines... (other than to make the wheels spin like billy-o...)