Invisible,
My experience in dealing with Ich is that any fish showing the white spots can transfer the more mature form of the illness (the white spots) to another tank, even if it is brand new. I am sorry to admit that my very first fish were 5 glass fish that were died in neon colors (I know realize how wrong it is to support this treatment of fish). Anyways, two of the fish showed signs of Ich very early, even though I did everything I was told to do in order to avoid the problem. Since my kids were already attached to the fish, I bought a 10 gallon 'hospital' tank to treat the fish along with another platy (I had decided to use the larger tank for a semi agressive community tank). Needless to say, all the fish ended up being infected and I had to scrap the whole tank and clean them out. Since then, I have had no problems and I am pretty sure that it is due to the use of a small amount of aquarium salt every other week (about 5 tablespoons for my 55 gallon tank).
From my experience, I would have to say that you should treat the tank with the infected fish in it and not risk moving them to another tank unless they are going to by themselves until cured. Another thing I learned from this experience is that the Ich cure tablets (of various brands) not only dye the water for a period of time, but also will dye any air tubes you may have 'hidden'. I have two air stones in my 55 gallon tank and even after changing the clear tubes, the stones held enough of the Ich cure to re-dye the new tubes. Just thought this would help since it cost me some money that I wasnt expecting to spend.