Everything affects efficiency.
I think you may be confusing effiiency with effectiveness. A dragster is not very efficient, but very effective. I was just trying to say if the only change is efficiency then the prop will load the engine down more than the less efficient prop. Of course you could try to prove that wrong by comparing it to a huge 0 pitch paddle bladed prop. Which will indeed load the engine down more, but thats comparing apples to oranges. If you take a basic design and improve efficiency it will do more work and work will load down the engine.