"I would conclude that not cooking makes no difference for a few days, but on a long hike it likely would."
On the CDT this year I went no-cook for nearly the first thousand miles, nearly 2 months. It was fine for me. I had planned ahead of time to get my stove in a resupply box after I got through Yellowstone N.P., and I did, but in fact I wasn't looking forward to it particularly. At the same time, I was quite happy to alter my diet and (dinner only) eating habits once I had it. I sort of missed the efficiency and "no fiddle" aspect of going cookless, but appreciated the food variety from what I had been mostly eating.
Sadly, the place I got my stove had no alcohol fuel for sale, and since my resupply box provided me with "really need to be cooked" dinner meals, I used slow-heating and heavy sterno in the Wind river range until South Pass City, and then resumed eating cold again until I could get some HEET (fuel) in Rawlins.
Anyway, bottom line for me this year was that eating cold seemed to work just as well for a longer period as for a short. One key factor here is that even on a long hike, a person goes in to resupply and eats as much ("town food") as possible when doing so. So it's not really "cold dinners every night" for months. I guess another key is not being terribly picky about dinner main meals. I found that I could happily eat just cold Idahoan brand potatos or "tuna with some sort of starch" (bread, crackers, whatever), just mostly alternating those two every other night. Each to their own!