I remember very fondly the days when all Water cooling was home made so far be it for me to discourage you, My first WC system was hose from lowes, a small submersible aquarium pump in a bucket, a radiator from a pinto and the Block I made from sheets of copper soldered/brazed together then pressure tested with a bike pump over my sink, my hold down was random parts from my junk drawer and plastic washers assorted dry wall fasteners and whatever else I could make work I got a Pentium 66 up to 100 and was ever so proud.
If you want to build your own go for it but I agree the factory build ones are cheaper in the long run unless you have a CNC end mills and a Vacuum form machine in your shop.
As per you design I don’t think a simple coil of copper tubing would have enough surface area to disapate much heat you could solder/braze some fins on it and that would help but a basic radi at the junk yard would be cheaper and much better if you are truly bend on making it your own.
If not get good air cooler or a RS or XPC kit