-----------------
SCENARIO: A plane is standing on a runway that can move (like a giant conveyor belt). This conveyor has a control system that tracks the plane's speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

Will the plane be able to take off?

-----------------

Here's my position:

The plane CAN FLY if.... see below.
The plane CAN NOT FLY if.... see below.

Here are the facts, which both CF and CNF folks agree on (I hope!)

FACT #1: Airspeed is an essential element to flight of a fixed-wing aircraft.
FACT #2: Groundspeed is irrrelevant to flight. It's only relevant if you actually hope for a plane to do anything except hover in mid-air.
FACT #3: AIrcraft use a Pitot tube , usually mounted on the wing, to measure airspeed.
FACT #3: Aircraft use GPS and radio-based distance measuring equipment to measure groundspeed.
FACT #4: In the absence of wind, airspeed and groundspeed are equal.
FACT #5: On an aircraft, wheel RPM, or wheelspeed, is irrelevant to both groundspeed and airspeed.
FACT #6: Airplane engines apply thrust against air.
FACT #7: Drag resists motion through air.
FACT #8: Friction resists motion on the ground.

-----------------

ASSUMPTION #1: The pilot knows how to operate the aircraft and can successfully take off on a normal runway.
ASSUMPTION #2: Windspeed = 0mph
ASSUMPTION #3: The plane has wheels.
ASSUMPTION #4: The wheels are the only part of the plane in contact with the conveyor belt.
ASSUMPTION #5: The moving conveyor belt does not create wind that has a significant impact on the plane.
ASSUMPTION #6: The tires and wheel bearings on the airplane are NOT frictionless.
ASSUMPTION #7: There is a physical limit to the maximum RPM that the plane tires and wheel bearings can rotate before failure.
ASSUMPTION #8: Based on the question, "Will the plane be able to take off?" we only care about FLIGHT. By association to FACT #1, we therefore only care about AIRSPEED.

-----------------

CONCLUSION #1: Based on ASSUMPTION #8, "plane's speed" means AIRSPEED.
CONCLUSION #2: Based on ASSUMPTION #2 and FACT #4, groundspeed = airspeed.
CONCLUSION #3: Based on CONCLUSION #2, "speed of the conveyor" means "negative GROUNDSPEED".
CONCLUSION #4: Based on CONCLUSION #2, the plane MUST ALWAYS HAVE a measurable groundspeed and airspeed or the conveyor would stop moving.
CONCLUSION #5: Based on CONCLUSION #4 and ASSUMPTION #5, the conveyor MUST ALWAYS HAVE a measurable negative groundspeed, but NEVER HAS a measurable negative airspeed.
CONCLUSION #6: Based on CONCLUSION #3, ASSUMPTIONS #4 and #5, and FACT #5, the conveyor does not negate airspeed.
CONCLUSION #7: Based on CONCLUSION #4 and CONCLUSION #6, the plane moves forward.

THEREFORE... the ANSWER to the question is:
Yes, the plane takes off if the thrust from the engine can overcome the wheel bearing friction and propel the aircraft to liftoff airspeed before the runway ends or before the tires and wheel bearings fail.
No, the plane does not take off if the engine thrust is insufficient to overcome wheel bearing friction before the runway ends or before the tires or wheel bearings fail.