By "power bank" are you talking about the power supply? Yes it should work as long as you have it turned on first, but it's not really a good idea, you will have a power supply sitting in the open and that can lead to all sorts of issues like some heavy duty shocks to you if you touch it and it's not grounded properly or if something spills on it, etc... Plus you will need to run the power cable inside your case from it. Better to just replace your power supply with one that has more connections.
Or you can just convert your current drive into an external one and use USB and a normal power brick.