Not necessarily. Many backup generators can only run for whatever the insurance estimators have calculated is the time required to restore the grid connection and that's it. For example one common means of generating backup power is marine diesels, which are readily available. These use the ocean for cooling. If you're using them to power a data center you need to provide cooling water to run them, and when you've run through that they shut down. That's just one example, but in general you can't run backup generators indefinitely.