No. I detest and don't use my freezer's ice maker. I just raise the on/off (or full/empty arm so the icemaker thinks the bin is full. Since they are built that way, and since the water pressure is pretty low, I don't believe - and I am trusting my new hardwood floors to this, BTW -any further action, aside from getting a bottom freezer, no icemaker,old-timey Amana refrigerator/freezer. But that isn't to solve the ice maker issue, it's to have an efficient means of refrigerating more in less floor space than a moribund side-by-side possibly can.
No, typically your shut off control is in the icemaker itself. Often a wire that "reads" how high the level of the ice is. You will most likely need to cap the water supply line. This could be easy or difficult. If the supply line is threaded you may be able to buy a screw on cap, otherwise you will need to solder on a cap.
Hi, I am almost sure you must cap it off, if not where will the water go and how will it stop running, if you do not turn the water off leading to the icemaker. Call a plumber or your water company. Take Care!