Does prolonging the primary ferment change the flavor of the bread?
That is, instead of doubling the dough if I wait until it triples or quadruples will it taste any different in the end?
The short answer is yes, it will change the flavor.
I'd be a little nervous about letting it triple or quadruple. At some point the yeast will consume all of the sugars near it and start to die off. You can end up with a sluggish final rise and a bit of a hoochy smell. I know whenever I've let my dough go too long and found it collapsing in on itself, after the final shaping it just didn't have much oomph left in it.
You can definitely prolong primary fermentation by punching down (or preferably, folding) the dough two or three or four times and letting it rise some more before finally shaping it. Refrigerating the dough will also stretch the primary fermentation for as long as you like, even a few days.
I take it that punching down or folding then redistributes the sugars to prolong the ferment.
You can mix the ingredients together so that all the flour is in contact with the water and then let that sit overnight to preferment. Then, develop the gluten as you would usually (Use a machine, hand knean or stretch-and-fold). After that, continue as usual - preshape, shape, final proof, bake.
That will give you the benefit of a long primary fermentation without as much danger of overproofing (building up and then breaking down your gluten) since you only develop the gluten after the prefermentation.
If I don't use that technique, I use the menthod Floyd mentioned, by putting the dough in the fridge for a long fermentation. It depends. I use both methods.