To me, this seems like allot of expense for a $100 fermenter. You could probably find a craigslist fridge for cheaper. SS coil and fittings are expensive. I would almost go the route of the SS Brewbucket, would end up costing the same and fit in your fridge.
The idea will work though. Kind of...
someone recently showed a foam board box that went around a wall mounted fast ferment. Used frozen bottles of water to keep things cool. Cheap and easy