Hi, welcome to the forums! Yes, re-rolling the dough, particularly if you dust with flour, can affect the texture of the dough quite a lot. Working any dough with gluten in it activates the gluten and makes it tougher (more likely to spring back); likewise adding flour while dusting will dry and toughen the dough. And yes, resting and/or chilling the dough can help relax it to a certain extent.
That all said, I roll at least a few times, keeping flour to a minimum and I am fine. In fact, I generally like the performance of my dough better on a second roll or third roll, because the slight amount of added flour makes the dough spread less and hold its shape better.
Every dough is slightly different, but if you bake off and taste small pieces as roll, you'll get the best idea of how your dough responds to the added handling and flour.