If a tube with spiral cut inner walls was filled with water and another tube of a smaller diameter with a spiral cut outer wall was placed inside the tube, but not touching the inner walls of the larger tube, and then spun... would the spinning water be able to move upward... against gravity?

no, i highly doubt it..... what gives you the idea, what force is there which is strong enough to break gravity? or to counteract gravity's field... to be precise

no, i highly doubt it..... what gives you the idea, what force is there which is strong enough to break gravity? or to counteract gravity's field... to be precise

 

Don't be so sure, gravity is deceptively weak and in many situations easily counteracted.............

Though I can't yet come up with a physically correct explanation, I think this might be one such case.

What if the tubes were in a "U" shape and the water started from the top of one side... would gravity and the spinning tube be able to move the water?

I know this for sure because I once calculated it, water in a spinning U-Tube does rise up. This is due to centrifugal force on the water in the lower horizontal part which pushes up the water along the vertical sections.