There's tons of nitrifying bacteria in the water column. How do you think it spreads and travels through the sump and that tanks? It doesn't take long for it to reproduce either, as long as there is food for them consume. As long as you aren't throwing 50 fish in the QT, your QT should easily handle the bioload of a fish that needs QTing. I'm sure there is more bacteria in 20 gallons of tank water than there is in a filter sponge that is sitting in a sump.
Sorry, but I totally disagree. There is a
minimal amount of bacteria in tank water and using cycled tank water in a QT tank does not mean the QT tank is cycled too. Bacteria grows on surfaces, like rocks and sponges. There is certainly not enough bacteria in free floating water to control ammonia. That's why they sell live rock, if it was as simple as adding cycled water then they wouldn't sell LR, they would only need to sell live water. Having the forethought to put a sponge in the sump of your DT is the BEST way to have an instantly cycled QT tank. Of course you can use a piece of LR but that rock should never go back in your DT, so you're basically wasting the LR rock unless you cook it afterwards. If you're not using some type of sponge filter or don't have one on stand-by in your sump you MUST test your ammonia several times per day and be prepared to do WC's daily if needed in the QT. This is the only way to guarantee your fish will survive in a non-cycled tank.
Personally, I always keep a sponge in my DT sump and can setup a fully cycled QT in minutes, as-needed. Sponges are dirt cheap, so never throw one back in your DT sump once you break down the QT. The sponge will be saturated with bacteria.
