Yes, the bacteria will eventually go dormant if there is nothing in there.
There are several ways to go about fixing this problem.
1 - Dose a little ammonia every few days. Twice a week adding the 'snack dose' as directed in the cycling article (see link at the header)... this will of course lead to nitrates sky rocketing (as you normally wouldn't be holding a cycle in a pattern like this indefinitely), and so you would need to do water changes on the tank fairly frequently to remove them... likely every 2 or 3 months (and definitely want to do a 100% water change before adding a sick fish).
2 - Depending on the filter set-up in your main tank, you can add the filter media from your QT to the main filter and keep it cycled that way. It may or may not have enough bacteria for the QT when you need it, but it will definitely hold some and can kick start what you need in the hospital tank.
3 - Move extra filter media over from your main tank into the QT to deal with the extra ammonia.
Personally, I wouldn't be running an empty tank just in case I have an issue. But, it is a great thing to have a QT available when needed with all the relevant parts. The good news is that they can be REALLY fast to set-up if you have all the pieces.
1 - You can just use water from the main tank to fill the QT, or about a 50-50 split with fresh tap. This means that your fish will be immediately (or almost immediately) acclimated to the QT, as its the exact same water and the exact same temp. You can place the heater in the tank to maintain the temp - or to bump up or lower the temp as necessary for your particular ailment.
2 - Once the water is in place, and the fish, the filter can be set-up using the spare media in your main tank, or anything else.
3 - Add some floating plants from the main tank, if you have any, like anacharis, etc. as this will give the fish a little cover and give them a stronger sense of security.
4 - Keep the tank in the dark. Dark tanks are better for the fish than bright lights when already being stressed by disease and isolation.