Can having one leg that is three-quarters of an inch shorter than the other cause a disc to become herniated in the low back?

This may not cause a disc herniation, but it could contribute. The shorter leg tilts the hip and pelvis down on that side. This tends to put extra pressure on one side of the disc, making it more prone to injury as time goes on. It's much like the alignment on a car. Poor alignment won't cause a tire to blow out right away, but after a while there may be enough wear and tear that you notice problems. Keep in mind, however, that no studies have been done to prove this.