Can the body's immune system fight off a kidney infection? Just curious.

Need clarification. If you're talking about pyelonephritis, an actual kidney infection, then antibiotic use is absolutely essential to management. If you're talking about a urinary tract infection like what most people get, then it depends. Asymptomatic women don't need to be treated but asymptomatic men should. Both symptomatic men and women should get treated.
Kidney infection. If you indeed have a kidney infection do not depend on your body to fight this off by yourself. Get checked.