I just did the trip you are describing two months ago with two friends. We used nitrox on every dive. We were the only ones on the boat who did so.
We did 11 dives in 3 days, and the dive sites generally started pretty shallow and got shallower. They pretended there is a PADI rule requiring each successive dive to be shallower then the one before. (There used to be such a recommendation, but it has been considered obsolete for over a decade.) They had a number of other policies that limited both your dive times and your procedures (like a mandatory 5 minute safety stop instead of 3). I believe their goal was to make sure that there was no way on Earth that anyone could possibly get DCS on the trip. I believe our group generally did our dives deeper than the rest and stayed at those depths longer, but I can't be sure. If I am right, that was the only advantage to the nitrox on a dive by dive basis.
On the other hand, if we go into the realm of the unproven and possible placebo effects....
I did the same trip 13 years ago, when I was younger and fitter. I did roughly the same dives, and I did them all on air. Every night I was thoroughly exhausted. On the last night I got up from the dinner table before dessert and slept through the night. On this trip I was having a wonderful time chatting with people well into the night each night.