It should as long as the laptop is connected to the power adapter. Who knows which device will end up charging if the laptop is not on the power adapter. The safer option would be to connect it to the power adapter to charge it....it would likely charge it faster as well.
Personally I would not trust unknown Chinese products since most of them are pure junk and many times very dangerous. Keep in mind the majority of electronic products on Amazon are pure junk....many of them are even dangerous and Amazon doesn't remove them even when informed of the danger. Plus the Lithium Battery in that item likely isn't of very good quality. That Amazon product page you linked shows that item as a frequently returned item. I definitely would not attach it to a $500+ device and risk it damaging the more expensive device.
The lack of clear detailed product information is a red flag. Don't expect any support from the manufacturer.