They should react the same within a reasonable margin of deviation. They won't be dead-on, but they should be close.
Best you could do to try to ensure better success would be to mark your clamps and fixtures and trussing and other stuff to try to line things up the same each and every time.
I stack my movers on my speaker stack, and that works fine, and as I'm at the same venue quite a bit, my rig is fairly consistent, enough where I'm fortunate to NOT have to adjust stuff.
In the case of touring, Serra Ava is right that he would likely need to adjust stuff from venue to venue. Trusses not hung the exact same height, angles of mounting slightly off... Nothing major but could be if not dealt with.