Most of the posts assumes that the electrical outage is localized, which isn't the point of this post if I understand correctly.
The answer is not possible. If there is no electricity, then Bitcoin cannot function. The same happens if there is no way to communicate with others as the network cannot transfer information.
Exactly, pretty weird that when clearly the OP says no energy something it's just that the power grid is down and they as an individual will get a new power source. But what about the others, miners, nodes, what about the guy who would receive that transaction, how is he supposed to get power?
The clear answer is that Bitcoin can't exist without electric energy just as card payments will not.
Bitcoin definitely can not work without the energy but since there are many ways to acquire energy, then bitcoin can still work using those alternative method.
And how can a protocol that is a bunch of code be able to acquire energy on its own?
The question was pretty simple, can bitcoin work without energy? No, it can't!
Until Bitcoin Core comes with a pack of nanobots that on install they strat building a solar panel and a wind turbine connected to your computer the whole network will still be depended on the power grid, just like every dan thing in our lives, from the coffee maker I just used to the computer I'm typing this answer.