Ditto, the above. Some devices, such as the Light & Motion Rando 500, can be charged and run simultaneously, but only at low power, and only with a special USB cable. With ordinary USB cables it can only be charged.

I've checked all of my devices -- lights, computer, video cameras -- and only some can operate normally while being charged from a USB battery pack. Price of the item doesn't appear to be a factor. I have an inexpensive helmet light that can be charged and run simultaneously.