If you tie a 100 foot rope to the tail of an airplane (or some other
part of the airframe), attach it to a good strong post, and run the
propellor up to whatever rpm is available, is anyone claiming the
airplane can then lift up say a feet off the ground?

(Assuming the tail doesn't tear off)

(and, a conveyor belt under the airplane is optional)

Depends on the airplane, if a plane is built in such a way that it can
actually attain enough lift just from the prop wash alone than yes.

The Monk