Ok, now for the explanation for anyone who hasn't taken physics.
First of all as many people have said the wheels are not driven. Also, what makes a plane fly is the air moving over the wings, this is called LIFT.
Anyway, the friction force generated by the wheels spinning will be minimal, like the hot wheels example the wheels are free to spin (unless the brakes are applied). The friction force here will be MUCH less than the drive force (generated by the engine).
The plane will move forwards on the 'runway' (aka treadmill) just as nothing was different. The only real difference is the wheels will be spinning at 2x the normal take of speed. BUT, this doesn't matter because the wheels are just freely spinning. Assuming the wheels can spin fast enough the plane will take off. Anyone who thinks different needs to go take a physics class...
F=MA
If we have two forces we can say F1>F2 so we can also say A1>A2. Lets just throw some junk qualifiers in here. The Force of F1 = 10 kg*m/s^2; F2 = 1 kg*m/s^2, M = 1 kg.
SO A1= 10 m/s^2 A2 = -1 m/s^2 (Because it is exactly in the opposite direction)
If we add A1+A2=AF -> 10+(-1)=9 m/s^2
Unless the airplane is tied down or the wheels can not physically spin at 2x normal take off speed the airplane WILL take off.
I haven't posted here for a while, but I really get sick of reading this "no it won't" crap. So STFU, GTFO, GSYGD!