The Amazon posting does not claim that it will charge the light while it is in use. The seller might not understand that the restriction on charging while it is in use is built in to the UT800 software. I would be surprised if it worked while the light was operating.
I just got a UT800 (£100 in the Sigma Sport Black Friday sale, great deal), and thought I'd give this a go with an external battery pack. When you start to charge it the light turns off, when you stop charging the light comes on again.