Reminder that unless you are protecting the lives of others, no job is worth your own life. Keeping a hospital online to keep patients alive? Sure, I might stay through a hurricane for that. Keeping email online for Helen in accounting? Nah, that can wait. We have DR plans.
Also, you don't significantly increase a generator's efficiency by removing the load. In fact, they need to have a minimum load to run properly (https://en.wikipedia.org/wiki/Wet_stacking). If you wanted to save fuel, you'd have to shut it down completely. If you wanted to ensure continuous operation, you'd already have a fuel truck on standby to go in behind the hurricane and refuel.