heat - Can I draw power for a component while this charger is charging the battery?

So I am working on a design for battery-heated wrist warmers. My mother has Reynauld's and arthritis, and as winter approaches it gets much worse.

My basic design is that I will take a form-fitting sleeve (made from a shirt or tube sock), weave nichrome wire through the sleeve, wrap thinsulate or space blanket around that, and then fix a nice-looking knitted wrist warmer over it. At the very least I think it would be a good start even without electric heating.

For the electric heating, I am thinking of using a 1000mA LiPo battery, a button switch, and a USB charger.

Ideally, the charger will charge the battery while also providing heat. My specific question is: can the charger I linked to provide that? In a more general sense, I would appreciate any suggestions you might have!

Thanks, and happy holidays!