When a herniated disc causes sciatic pain, will the opposite leg feel shorter over time?

No. Probably not. The disk herniation has no effect on leg length. I have not had a patient complain (or notice) of a leg feeling longer or shorter if they have or have had radiating pain (sciatica).
Disc. Perhaps your affected leg feels longer because you have weak muscle that flex (bring up) your ankle. If so, you should have it checked.