This channel is a treasure trove for answer to similar questions:

[1] Can lego break a steel axle?

[2] How much load can the smallest lego gear handle?

[3] Testing lego gear and pulley systems

[1] https://www.youtube.com/watch?v=jRn5waE0qfk

[2] https://www.youtube.com/watch?v=YjhOGoZ-bNI

[3] https://www.youtube.com/watch?v=bWgTRHH656Y

No, because the plastic gears connected to the drive wheel would snap under the immense torque.

Right, sure. In my mind, I was more interested in the relationship between gear-ratios, torque and the displacement of weight.

What if the motor gears were infinitely strong? That is: is the power output of a small electric motor theoretically sufficient to drive a tank up a hill with an arbitrarily large gear ratio?

You can trade torque for speed basically. So yes. "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world". That being said it would be so slow that you'd probably break something before you've moved a millimeter.

The same Youtube channel demonstrates how to use gear reduction to increase torque and bend a steel bar with legos: https://www.youtube.com/watch?v=jRn5waE0qfk

Yes. it would be equivalent to Archimedes’ claim “Give me a place to stand on, and I will move the Earth” (https://en.wikipedia.org/wiki/Archimedes#The_Lever)

Certainly. It would just happen arbitrarily slowly. (And, at that scale, other factors would come into play; the soil would deform under the wheels of the tank before it moved any distance, probably)