I do think his behavior will subside once he is not only better acclimated, but getting plenty of exercise! I'd take him out on the leash as soon as possible, as most cats will begin to associate "harness means I get to go OUTSIDE" pretty quickly, and unlike a certain bunny of mine*, will be too concerned with exploring things to be bothered fussing with the harness and leash.

*Miss Hoppy, now at the Rainbow Bridge, was so bothered by the fact that the harness mussed her fur that she turned into a fur-covered brick. Yes, if I pulled hard enough she'd move, but would NOT hop on her own. We gave the harnesses to a shelter, and took to fencing in an area outside for her to play in, only while supervised!