Could putting a stent in my renal arteries cause me to pee more?

Probably not. Renal artery stents can improve function of the kidney. Increased urination probably a result of increased hydration (fluid intake).
Possibly. I doubt this has ever been looke at. In theory it seems possible for the kidneys to make more urine after stent placement perhaps for a day or two. After that your body should have reached an equilibrium and normal urine output levels. If your kidneys were failing and have improve in function after stenting, it is conceivable that your urine output will improve with improvement in kidney function.