Modding Bose QC20 to use dc power?

If the battery is still alive, you can charge it while using it. A power bank, because an AC based charger can introduce buzzing. But not all power banks are likely to do it, since it draws very little current. My best performing power bank for small current will work for a while and then I have to push the button so it starts again.

I have read somewhere that Bose put limitations in place so it won't work if the battery is actually dead. They put in other limitations, so that's not unlikely.

You've probably made other arrangements, but putting it here for others with similar questions.