No, it won't.
What you are describing is a part-time 4WD system. The SR5 and Trail Edition have a part-time system. In a part-time system, when you put it in 4WD, the front and rear driveshafts turn at the same speed. Since the rear wheels take a shorter path around a corner, the rear driveshaft wants to turn at a lower speed than the front driveshaft. Offroad that is fine, as the tires just slip. On the road, it can bind.
But the OP has a Limited. The Limited has a fulltime 4WD system. He can put it in 4WD and leave it there on dry pavement forever without any damage to the system. The Limited has a Torsen limited slip center differential. That center diff allows the front and rear driveshafts to turn at different speeds.
As long as he does not lock the center diff, he can leave it 4WD all the time. Locking the center diff makes the front and rear driveshafts turn at the same speed, just like a part-time system. You should only lock the center diff when on soft surfaces (for example, dirt or sand) or when only traveling straight.