There are also a lot of experienced fish keepers and reef keepers who think it's pretty foolish to think you can completely remove/prevent introduction of ich in a tank. The important thing is keep healthy fish and crystal clean water.
The hospital tank is not a bad idea, but make sure you have a big enough one and have plenty of filtration capacity to keep water quality high. Moving six unhealthy fish into a 20g tank with inadequate filtration sounds to me like a recipe for trouble. Not to mention that catching your fish may be difficult.
I know opinion on this subject is not unnanimous, but I really think the primary concern is not whether there's any ich present in the system, but whether the fish are generally healthy and the water is free of any measurable ammonia, and nitrites with stable salinity and temperature, and nitrates as low as possible.