Okay, so I'm not a CFI or anything here, but in a 182... if you have the student jockey the throttle to get back to 80 knots or so in the pattern, they probably could "get away with" never touching the prop lever at all. At least at first.
No it's not good technique for later, and not as nice to the airport neighbors for noise, but on the older 182s with 2600 RPM a full power climb-out to pattern altitude and then pulling the power back with the throttle and leaving the prop pitch alone, would be fine... In the pattern.
In a rental (owners would cry...) just leaving the cowl flaps wide open (especially in summer) would also be "fine". Again not proper technique, but it'd be an easy way to lower the student's workload for a while and then introduce the proper use of those two extra levers a little later on. Bad for their "muscle memory" and checklist use, though... so you Instructors would have to decide if you could handle explanations that you're making things simpler for them, or you could take the approach that they call out the checklist items, and you'll handle the prop and cowl flaps for them until later...
Seems to me, anyway, that the 182 is a bit simpler in this regard than some complex aircraft. It'd handle the "abuse" of not paying attention to the prop or cowl flaps in the pattern just fine -- if you're trying to lower the workload on a new person to the aircraft. My experience here is 182-specific. There would probably be limitations on the 182RG and T182T but again, I can't imagine the student couldn't just slow down with power in those aircraft too. Prop full forward around the pattern doesn't seem problematic in the 182 variants to me. No need to do it at full-throttle though.
The more worrisome part would be teaching a primary student not to ever land on the nosegear in a 182 unless they have a very big wallet. Firewall damage is pretty common. That and if you're in an older one with 40 degrees of flaps, they'll have to get used to how quickly you go from level flight to a high sink rate if you flare too high... which is not a good idea in a 182 with the power all the way off and flaps at 40. Flare it high and you're going to arrive pretty hard. Henning's been talkin' about this in the thread about all landings being "short field"... if you learn where this point is and can "feel" it in your aircraft at all weights... as your butt starts to fall out from under you, you can add a touch of power if you must... but a student is going to be figuring out that "feel" and that could be really hard on the gear and tires on an older 182, and if they don't keep the yoke back, the nosegear and firewall. I'd be more worried about that with a primary student.
I know I bounced a rental Skyhawk or two off their nosegear while doing go-arounds in my solo days... and no, I wasn't happy about it. The power was already up and I was rejecting the takeoffs both times, but hadn't pitched up properly, and didn't hit the nosegear hard, but I was pretty hamfisted back then. (My instructor was always weirded out that I loved 40 flap landings in the Skyhawks, and had that sight picture nailed and made good landings that way all the time, but go to no-flap landings and I was all over the place back then.)
Fast, flat, landings have never been my forte'. I'll freely admit it. Dropping like a rock with flaps and slips from pattern altitude turns to final, I do that really well. No, I don't know why. Back then fiddling with pitch over the runway while bleeding off speed (wasn't nailing my approach speed) was the most likely problem. I absolutely LOVED the speed brakes in glider flying... modulating them to hit a specific point on the runway... that's fun.
Anyway... primary and transitioning students in the 182 have to learn how to get the 182s "heavy" yoke back and keep coming until it's all the way back in their gut for "full stall" landings and to "protect" that nosegear. The only time I don't have the yoke in my gut at landing is if I really badly need some additional speed for more rudder in a nasty crosswind or I'm landing really long and flat for one of those "greasers" that you cheated bad to get by chewing up 3000' of runway to get it.
I'd be really nervous letting a primary student fly *my* 182 without a CFI I really trusted to stay on that yoke and keep them off the nose-gear in the flare. And then they'd have to solo and... all bets are off if your airplane will come back without firewall damage... yikes. I'd really prefer they beat up a Skyhawk a little first.