If the gas station has a generator to keep the gasoline pumps and the store operating then yes the gas station and gas pumps will work during a power outage.
Some gas stations have generators and some gas stations do not have any generators so not all gas stations will be open or work during a power outage.
The gas pumps require electricity to operate them and if there's no electricity to operate the pumps then they will usually put a sign on the pumps noting they are out of order.
The store may also close until the power comes back on if they don't have a generator.
I've been to some gas stations that had backup generators while others did not so it can depend on the gas station.