We used to run 23mm on our tandem because they were fast. It was noticeable, coming from 28mm Gatorskins. Very light tires, very high pressure: 140 front and rear. Also a 300 lb. team.
Not all 23mm tires will take that pressure, so yes, 23mm tire model does make a difference. TG used to run 23mm. A local long distance racing team, heavier than we are, ran the identical tires with great success. I'd call a record a great success.
However, a thin casing, high pressure, and a lot of weight per tire made for a delicate tire. Too many flats, too many sudden deflations from cuts. We went to 25mm at 115 lbs. Much better and still fast. Now we are running PRO4 Endurance 25mm, which measure 29mm on our new 23mm rim. We run the PRO4 tires at 110 on 19mm rims and 100 on 23mm. Bike still feels fast, and way fewer flats, which increases our real-time speed. 2 minutes is forever on a group ride, and 10 minutes is never see them again.
The only times we've had a pinch flat with any of these tires was when Captain screwed up and rode over a large rock with one side of a tire. Since one runs a smaller tire at an appropriately higher pressure, pinch flat likelihood remains the same. I do call "up" if I see it coming. I use tire size * pressure = 3000 for a tandem approximation. So we've had a couple pinch flats on the tandem as well as on my single bikes. Never an blow-off sort of pinch flat. I can't imagine how that could happen. If a tire can hold air pressure inside a tube, the tire should be able to hold pressure outside a tube. I don't see the difference. We had 3 heat blow-offs before we went to Deep-Vs, all with 25mm 4000s, but never had a tire come off the rim. Always got it stopped.
We still carry a 23mm light tire for a spare. Works fine. Gotta have a good pump, though.