You can see that the unrested dough up top is freaking out. It's all rough and jagged because the rolling has essentially snapped those little gluten bonds in half. But as I continued to roll it through increasingly thinner settings, it took on a much smoother texture. By the end, there was very little visual difference between the two.
Ultimately, I rolled out and cooked all six doughs. Was there a difference between them? Yes. The dough that hadn't rested at all was a little harder and firmer, a little more rubbery. The doughs that had rested for an hour or longer were almost identical. It's sort of like the difference between blender pesto and mortar-and-pestle pesto. The former isn't bad but the latter is definitely superior. It also takes a lot longer. In this case, you're not stuck manually grinding something up, but if you're looking for a quicker method, this is your cheat. No rest, or just a few minutes, is not going to make inedible pasta. In fact, it'll make pretty damn good pasta. But it is a trade-off and only you can say whether or not it's worthwhile.