I know of four reasons to let your unyeasted dough sit for a while:
Gluten relaxation. user9074 has already explained this. The gluten that has formed during kneading needs time to relax, which will make the dough easier to work with and cause the cooked bread to be more tender.
Gluten formation. Kneading isn't the only way to get gluten molecules to link up. Time works well too. There are "no knead" bread recipes where you just mix the dough and then let it sit in a cool spot overnight, or in the fridge for a day or two. A few hours sitting on the shelf may improve your dough by letting more gluten molecules connect.
Autolysis. The flour itself contains enzymes that will break down some of the starch and proteins in the flour and improve its flavor. The effect of autolysis will be greatest if your dough doesn't include salt, but it may be a factor even with salt added.
Hydration. It takes time for the flour to really absorb the water that you add. If you've ever made a pie crust you'll know that pie dough changes dramatically during the rest period. It becomes soft, smooth, and pliable. That transformation happens because the rest period gives the flour time to soak up the water. I expect that giving your dough time to hydrate will improve it as well.
These are just some reasons why resting could improve your end result. Ultimately, there's an easy way to answer your question. Make up a batch of dough and give it time to sit. Prepare another batch just before cooking. Cook up some parathas from both batches and compare. I bet you'll find a noticeable difference.
All that said, I'd also bet that unrested parathas are better than no parathas at all. Don't let short time prevent you from making them any way you know how. If you're into experimenting, there are ingredients such as dough relaxers that you could add to get some of the same benefits that you get from a long rest, but in a shorter time.