The usage described is called "pass-through charging." The good news is that the PowerPack 10K, 10K USB-C, 20K, and 20K Pro all support pass-through charging. But, there are a few caveats to keep in mind:
1) You need an AC power adapter (power brick) with an adequate power rating. But, it doesn't necessarily mean using a wall charger with a lower power rating won't give you pass-through. The battery pack takes precedence when there's not enough power to go around. But, the battery pack will eventually get fully recharged, by which time, the surplus power will get routed to the device connected to the USB-A port.
2) In the pass-through mode, the output voltage from the USB-A port is limited to 5 volts only. For example, if you have a Samsung Galaxy phone, fast charging is not possible.
3) Use high-quality cables with low electrical resistance. The battery pack does not compensate for any voltage drop in the pass-through mode.
4) Most of our PowerPack's do not work as an Uninterrupted Power Supply (UPS). During the pass-through setup, if the AC power is cut, there will be a momentary loss of power on the output port of the PowerPack. That split-second loss of power is enough to cause a device without a built-in battery to reset.
If you are looking for a power bank that supports UPS and pass-through charging, take a look at the PowerPack Ambi.