No it will not. If we do not have electricity anymore, we simply cannot transact or mine Bitcoin until we have our electricity back. Unless we never have electricity again, then that is a different matter. But lets be realistic, that is not going to happen.

Bitcoin cannot become extinct unless everyone in the world suddenly decides to drop Bitcoin. And even then I am sure there will be a few dedicated people still keeping things going.

The most realistic scenario is that an alien race visits us and gives us technology that makes money completely redundant. In that case, sure. Maybe.