I guess that would depend on the manufacture of the shells. if you had 2-3/4" and 3" shells both putting out the same FPS, both loads would hit at the same time. Yes, the 3" shells have more powder and will kick harder, but that's because they have to push a larger payload of pellets (or buckshot in your case) out of the barrel. So to answer your question, no, you wouldn't get more range out of the 3" (in this instance), But if you had a 3" shell with a higher FPS than the 2-3/4", then of course you could get more distance. The idea of a 3" is more coverage, not more velocity or power. If you reloaded your 3" shells and kept the powder the same, and left out a few pellets (say a 1/16 to 1/8 of an oz) then you would increase your FPS and therefore your range.
As for real life experiences and opinions with buckshot...I've used two different sizes (00 and #1, mostly in 3") and have shot a good many deer with both. Some went down like they were pole axed, and others didn't. My wife took her first deer with a load of Federal 00 buck in a 3" shell. Yes it killed the deer, but when we skinned it, only one pellet penetrated the lungs. The others stopped between the hide and fell out as we peeled the hide away leaving nothing but large bruised spots on the rib cage. The deer was at what I would consider a reasonable range of 25 yds when shot. In another instance, a cop buddy shot through the rear window of a car (at close range) at a bad guy that tried to run them over. The suspect was "treated and released", he switched to slugs.
Hope this helps a little.