The general theory is that a wider rim should have the same tire casing running wider and have a better ride feel. For what it's worth I find the ride quality of Gatorskins fairly poor--you'll get a drastically bigger difference in ride quality switching to even Grand Prix 4 Seasons, which literally have the same puncture protection layer as Gators, but have better quality rubber which rolls a lot better, at a minute expense of puncture protection. You'll also get a drastically I honestly feel like Continental keeps the Gatorskins around just because they were early to the market for a significantly more puncture protective road tire that felt OK to train on, and so many regular road riders have used them for so long they don't want to scrap a cash cow. You'll feel a bigger difference with GP5000s or other supple, fast, everyday road tires. Also I like road tubeless, but I agree that if you don't feel that the sealant sealing small punctures is a major advantage, the more difficult tire mounting and need to add sealant probably outweigh the pretty modest other benefits, which can be made up in large part by using a supple ultralight tube.
Also unless your frame has clearance issues, most road calipers now clear 28mm tires which will vastly eclipse almost all factors regarding ride quality, with the only disadvantages being a small amount of weight, and possibly aerodynamic drag depending on rim profile.