If you were to reconnect your electricity after a shut off would the power company know?

Usually when the power utility disconnects your electricity, they remove the electric meter. Without the meter, there is little chance (if any) of gaining any "free" electricity.

They could also disconnect the "grid" to your residence at one of those outdoor sealed and locked enclosures.

Sometimes, they may put a lock on your switch box and accompany that with their "seal" that if removed, it will be rather obvious.

And if you get caught, you are going to be prosecuted for theft.