The tank was cycled ok, and now it's empty?? An empty tank (set up with water but no fish or added ammonia) can't cycle. There is no benefit to setting up a tank and running for a few weeks to cycle -- it can't happen without ammonia and bacteria. You could do a fishless cycle to get the bacteria going again. I have used Bio-Spira a few times very successfully, but I guess it's unavailable for awhile.
My mom wants me to bring my bettas to her house when we go on vacation, because she likes to take care of them, but this wouldn't be a good idea. If I take the bettas out of the tanks, and put them in bowls at my mom's house, then all the established bacteria will die in the tanks. (Besides, the bettas won't like the little bowls anyway!) Sometimes, if the betta is in a
QT bowl for only a few days, I still "feed" the tank a small amount of fish food. The resulting ammonia from the "rotting" food will sustain the bacteria for a few days while the betta is gone.
To answer your question, yes, the bacteria will die without a food source. The food source can be the fish, or ammonia you add as part of a fishless cycle. If the bacteria dies, then you have to start the cycle over.