The acoustics I have found in my reading indicates that reducing the diameter of the tube at the location of a note's "displacement anti-node" where the air molecules in the sound wave are moving the farthest causes that note to go flat. Reducing the volume at the location of a note's "compression anti-node" where the molecules are the most compressed causes the note to go sharp. It is logical to assume that these effects are greater when the tube is narrow where the dent affects a greater percentage of the diameter. Conversely the effects are less when the tube is wider since the dent affects a smaller percentage of the overall diameter. I don't know how one would determine which note or notes have a compression or velocity anti-node in the bow of a saxophone.
From my experience teaching school band I know it is quite common for the tubas and baritones to have several large dents in the bell bow area, and the intonation doesn't seem to be affected to a large degree although in a junior high it is hard to tell whether the poor intonation is the horn or the player.