Answer:
No, there is not enough current available from the USB port on a
computer to charge the Q2. As there is a fire risk if the Li-poly battery is
charged with a generic 5V, 1A mini USB charger, we can only recommend using the
official Q2 charger that was originally supplied with the equipment.
Unfortunately due to
the Li-poly technology used in the Q2, the battery is not a user serviceable
part.