It does not need to be cycled, but you need something to keep water moving (I use a little power head that I keep in my DT that is for a nano tank (think it was $25).
For me...Take tank out of storage in the garage....add water, my little powerhead and a sponge that I keep in my filter (that will have BB)...add sick fish...treat with hypo or copper...wait a month to allow DT to be Ich-free.
A 20g tank is $20 with Petco's dollar a gallon deals. Even if you got a cheap filter (maybe $25-$35 for a tank that small) or do the sponge and powerhead idea, you are up to maybe $50. If I have a $40-$50 fish, or two, that need QT, I'm saving money in the long run.
Better yet, QT fish prior to adding and treat if they get anything while in QT. That should keep most of the nasty stuff out of your DT in the first place.
Then there's always the "Don't QT, eventually get something that kills your fish, don't CURE the original problem and buy more fish and then cross your fingers that it doesn't resurface" method. $50 is good insurance in my opinion.