I did a test flight on a 172 or 182 years ago after major structural repairs. rim was hooked up backwards. Let me tell you how hard it is to tell your hands to move a control the "Wrong" way to make the airplane do what you want! The guys in the shop that put the airplane together were chastised that afternoon! Then again, I should have caught it on preflight.
I had checked all primary controls, just not the trim
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Assuming correct continuity a trim system should still be able to help fly if the elevator controls are reversed or unavailable. One check pilot I had required a demonstrated trimmed departure, approach, and landing. Power was adjusted as well to help stabilize. Made me a believer as a last resort.
Rudder can function to level the wings if the dihedral is sufficient and the ailerons not deflected too much. Something to practice to become convinced just in case....
Trim would work if you know about the problem.
Ditto on opposite control input.
But on takeoff? "Hmm, climbing too steeply, push the stick forward" resulting in more nose up.
I think the average person would stall & crash nose down before he even realized what was wrong.