I had mine put in while I was already in the hospital, but I'm sure it could have been done as an outpatient procedure. It was not even placed by a doctor, it was placed by 2 nurses that had gone to some special training. They rolled a portable ultrasound machine right to my bedside.
I don't know if one can reject the line. All it really is is an IV that is intended for longer term use. The main concerns with it will be, of course, infection and clotting over of the end that is in your body. It is put into a larger vein in your upper arm, so it's not like when they try to put in an IV line in the tiny veins in your hand or wrist. They cover the end that goes into your skin with a piece of gauze, and then cover the whole thing with a larger piece of adhesive. It's kind of like a clear bandage that is about 4 inches by 4 inches. Think of contact paper.

The only part that sticks out of this covering is the tube that they will use to hook the IV into I think the tube part was about 5 inches long or so.
I know it sounds scary, but mine really wasn't that bad.