Basically as the title says. We have semi frequent power outages where I live. The noise machine in my daughter’s room goes out and wakes her up. If I were to buy a USB powered one, plug it into a power bank like one of those 10000ma ones you get for charging cell phones, would it have continuous power. Basically like a cheap UPS
Yes, battery banks with at least two ports and pass through charging will handle it like this. The Anker bank I have (Anker 737) does this.
For long term use the battery cells may degrade in capacity and max current after a couple years of sitting at 100% charge, but that’s probably not too big of a deal for you since the noise machine is probably fairly low power.
Connect it to a smart plug that you set to turn off for several hours periodically. When it shuts off, the Anker will have to start using its own power for a while, and since this will occurr regulary, it won’t be sitting at 100% nearly as often.