While they do need oxygen to "eat" so to speak, they will not die within 5 hrs from lack of it. They will die eventually without it, but bacteria can go into a dormant stage without it for much longer than that, days even depending on other conditions such as temperature and pH.
And a filter turned off even overnight will not be completely depleted of oxygen anyway. Some dissolved oxygen will still remain in the water for quite some time.
You are right in one respect though - biological bacteria will not grow and function long term in an enclosed space like a filter without circulation. But skjl47 is also right that you will have some functional bacteria in a body of water like a tank even without circulation, because with enough surface area there will still be limited dissoved o2 in the water. A goldfish or betta bowl will still have bacteria on the surfaces.
However, you will have much more efficient growth and function with more circulation to raise dissolved o2 levels. That is why a wet/dry is much more efficient and effective than something like a canister of the same size, because you are heavily oxygenating the water. Water dripping down through holes greatly increases water surface area, which exposes more water to the air to create dissolved o2.
