If the plane can move at all, then it can take off. I don't have to run a calculation on how long the runway has to be in order for it to accelerate to lift-off speed. I only have to prove it can move at all. The distance it takes is of no consequence.

If it can move at all, then it can get enough speed to take off.

And if it can move under a "touch and go" scenario, then it can move from standstill, as well. The physics that allow it to move at all are the EXACT same, regardless to the initial velocity being 0 mph, 50 mph, or 2,000 mph.