Using a mobile phone power bank in place of AA batteries
No, there isn't. For most, they are a single Li-Po cell with a built in charging circuit and boost output, with auto cut off. They will boost to 5V typical. There are also larger 12V ones, or ones that can do both.

Some newer ones have auto-shut-off if they don't detect a significant load. That may be an issue. Stick to the dumb ones.

These are ideal for your needs.