Is it even necessary to clean a copper IC with PBW? What is PBW getting off your IC that you're concerned about having in your brew kettle? Is it the oxidation layer?
After use, I simply rinse the IC off with water. It tends to take on a mottled greyish-coppery color during storage.
On the next brew day, I hook up the IC to the garden hose. I rinse the IC with the water that flows out of the output end (to get the dust off of the IC). The IC gets placed in the boil kettle for the last 15 minutes of the boil--it gets shiny copper colored due to the acidity of the wort. I don't notice a greenish residue during storage.
Any problems doing it this way?
I wouldn't think so. Unless, you have something in your storage area that rinsing won't remove. I use a counter-flow, so I like to clean it pretty good before storing it, then prior to use I rinse, and then follow by running hot wort through (that I return to the boil) for sanitizing.