Q: While I'm recharging the PowerPack 20000, can I also simultaneously charge another device using one of the USB-A connectors?
A: The usage you described is called "pass-through." The good news is that the PowerPack 20K does support pass-through. But, there are a few caveats to keep in mind:
1) You need an AC power adapter (power brick) with an adequate power rating. A power rating of 30-45W or higher would be good. But, it doesn't 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 much power to go around. But, the battery pack will eventually get fully recharged, by which time, the surplus power will get routed to devices connected to the USB-A ports.
2) If the PowerPack 20K is completely out of juice, it might take a few moments for the battery pack to soak in a little electricity. The pass-through will then kick in, provided that an adequately rated power adapter is used.
3) In the pass-through mode, the output voltage from the USB-A ports is limited to the plain 5V only. There's no fancy fast charging or anything like that.