I remember some article of someone trying it, only to discover their power bank cut power for few milliseconds when you disconnected the external power supply, resetting the device...
i can attest to that. all of my cheap power banks demonstrate this behaviour.
more importantly, as the article suggests, it can be hard to know if the battery itself is powering the device while plugged in (while getting charged) or if there is a passthrough, a la laptop charger.