I thought of using copper pipe like that but its not cheap and in a fairly humid climate, I was worried I would still need a refrigerated drier. When I researched, the best place to cool air is before the storage tank where a precooler radiator is added in commercial installs. Ideally, water should be drained away before the storage tank.
So I added a 3/4" transmission cooler between the compressor pump and the storage tank so the fan that is part of the pulley could draw air through the heat exchanger. This has proved very successful. The top inlet is too hot to touch yet the bottom outlet is cool to the touch so its probably as effective or more so as your proposed pipework.
The mechanical autodrain removes some water before the tank. It could be improved by having a long riser after the autodrain to allow water to run back down to the drain. Because the compressor is not readilly accessible on top of the dunny roof, there is an electric timed autodrain on the tank drain. Then the air flows through a 1" pipe to the refrigerated drier that came with a pre and a post filter for maximum flow. The drier filters also purge occassionally.
This has been perfect in use for about 4 years now. The precooled air ensures the drier always hits its dewpoint for maximum water extraction and I've never had an issue with moist air and do not run any filters after the drier .