On Oct 2, 1:08*pm, The Natural Philosopher wrote:

No. Static thrust does no work any more than a labrador sitting on your
foot and imparting thrust, is doing work.

I agree with everything in your post, with one slight clarification
that I expect you'll agree with. Static thrust does no work on the
craft. It does do work on the air however (except of course in the
limit as you approach a 100% efficient prop).