Okay, another update to this hairbrained scheme of mine!
Turns out, the short answer to my question is: no.
Several of the replies above already anticipated this, but here's the whole story. I soldered a USB plug to the wire to my taillight so it would function the same as my headlight (but the taillight has no on/off switch). I plugged both into my large USB battery, which has two outlets. The battery has an on/off switch. Powered the battery on, taillight came on; switched the headlight on, headlight came on. Plugged 5v input from the dynamo into the battery; both lights were on, good and bright, so far so. Rolled the bike out to the driveway, and noticed the lights were off. WTF? On closer inspection, the battery was off. Turned it back on, got on, turned the light back on, and as soon as the wheel turned it was off again. Well, it turns out the battery automatically turns off its power outlet(s) when it is charging.
So I left the taillight plugged into the battery, and powered the headlight direct from the transformer thing. The only problem with that scheme is that I had to press the on button on the light every time I started from a stop, which happened about five times.
By the way, the power converter, or transformer, or whatever we should call it, is the silver box included in this set:
Generator Bicycle Bike Dynamo w USB Charge for Cellphone Mobile 12V | eBay

AC power comes from a Shimano Alfine dynamo hub; I'm not using the dynamo that was included in the photo.
The headlight is this one:
New CREE 1200 LM XM L2 T6 USB LED Headlamp Headlight Bicycle Bike Light 3 Modes | eBay
I don't remember what the taillight is; something similar to a Spanninga Pixeo.