Planted Tank Guru
Join Date: Jan 2010
Location: Contra Costa CA
Anything you place in the current tank, in the filter or the tank can start growing some bacteria. It won't grow much in a short time, but if it will be several weeks until you set up the new tank, and the new tank is a lot smaller, then that amount of bacteria would probably be a great way to cycle the new tank.
Bacteria will live on activated carbon. I just save it for an emergency, though.
Add any sort of sponge, floss, lava rock or bio media to the existing tank as a media for the bacteria to grow on.