Thanks for advice!
[MENTION=391744]catgita[/MENTION], to clarify, I know there are rechargeable lights that charge with a USB charger; but this is not that. My light has no internal battery. It's pretty neat but when powered directly from the dynamo and converter, it cuts out when my speed drops below something like 8 mph. That's annoying and means I have to mount it where I can reach it, so I can turn it on again when my speed goes up again. So it would be better to have a battery (or a capacitor) in there.

I did know, however, that the rechargeable ones won't turn on when charging. That's actually the reason for my concern. Is this a safety feature? If so... maybe this isn't wise?

[MENTION=197614]fietsbob[/MENTION], my longer range plan is to use two batteries as you suggest, and I have ordered two that are being shipped from China. But for now I have one biggish one. I thought I'd try this scheme out tomorrow and want to be sure I'm not going to ruin the battery.