THe biowheel is just a piece of strong pleated paper with only as much surface area as the paper's dimensions give. Its main benefit is the excellent air/water combination that it has as it turns. This does not mean that it will not continue to be a fine platform for bacteria if submerged in a tank. So, if you wish, you can submerge it in a tank and let it just float around. It will not be any better than any other media that you may have, but its bacterial colonies will not die out, either.
Go for it and float it........as long as you are sure there is nothing in the qt tank that needs to be sterilized and reset......
Is there any reason why you cannot simply add that filter to another tank? A little extra filtration rarely hurts, and running it would preserve the cycle perfectly.