They use automatically extracted DNA (purity of the DNA sample will likely affect shelf-life) and employ multiple different methods to quantify recovery (Gel, PCR on a housekeeping gene and SNP analysis).
The data suggests that RT/4 °C is fine for 6-8 weeks. I can confirm this from my personal experience. For longer storage -20/-80 °C are preferable. Their data show no significant loss even after 24 months.
DNA is also lost through binding to the plastic of the storage tubes. So you could think about buying non-stick eppendorf tubes.
Article Avoiding DNA loss and denaturation upon storage in plastic microtubes
Some people also add EDTA (1 mM) to decrease residual nuclease activity. However, this shouldn't be necessary for frozen samples.
Do you mean culturing for 72 h and then isolating the DNA or using the DNA 72 h after you isolated it?
In the former case it depends on the kind of bacterium and culture conditions, e.g. E. coli will have entered death phase after 72 h. This might severely reduce quality of the DNA isolate because it will start to degrade after cell death.
In the latter case yes, that should work. However, depending on how expensive/time-consuming your experiments are it might be advisable to check the DNA first or make a new preparation.