Is it possible for a stent to cause diseased legs?

No: Stents don't cause disease, but they can fail. They fail either because of scarring, clotting or progression of disease (atherosclerosis). Whenever stents are placed they should monitored on a regular basis in order to intervene before any of the above occur.

Not really: Once a stent is placed to treat a narrowing in a vessel, a reaction causing overgrowth of the vessel sometimes forms, which can cause the vessel to narrow again. This is called intimal hyperplasia. Smoking can cause this to happen faster. Notify your doctor if symptoms come back.