Yeah, you need to make sure your car seat works with your main car before leaving the hospital because they get upset when you bring a box with the car seat and base still in the box. They check and make sure baby is safe before you leave the campus of the hospital.
You do need to bring your car seat into the hospital after baby is born, they must mean installing the BASE of the car seat :) it's very easy, just buckle it in and make sure it's tight