Can a Plane on a Treadmill Take Off?

Actually, I believe you are incorrect. That passage only implies the
belt will move inversely proportional to the wheels on the plane;
meaning the delta is conantly zero. They never actually state the
plane is moving forward. Thus, with a wheel speed of zero, the delta
is still zero. Therefore, I would suggest the only correct answer,
based on that sole passage is, "no".

Now, if we look at the actual question posted on straight dope, the
answer is, "maybe", for many reasons. Having said that, we can
*easily* tear up the explanation provided on straight dope. Simple
fact is, Cecil makes a huge assumption which causes his whole house of
cards to come tumbling down. Simply stated, there is nothing which
precludes the belt from being motorized. Given a sophisticaed enough
implementation, one can absolutely state, the plane would never leave
the ground; assuming no head wind is involved.

Long of the short, there is simply not enough information to provide an
exact answer, other than maybe. If the belt is not motorized, AND the
plane is moving (positive delta), yes, the plane will fly. If the belt
is motorized, and it is intelligent enough to ensure a belt/wheel delta
of zero, no, the plane will never fly.