I think a short answer would be yes, but with caveats.
Many GoPros have been flown on high-altitude balloons to near-space and in close to vacuum conditions, using completely COTS assemblies (and therefore internal batteries). GoPros also work on the ground in vacuum chambers.
Alright guys, so the GoPro Hero 4 black would survive in space, but there are a few things to consider; you wouldn’t be able to record for as long because the camera would overheat due to the fact there’s no air to dissipate the heat coming from the sensor. Another thing is that the case was designed to keep the pressure out and not keep the air inside from escaping. So if you listen carefully you’ll hear the air escaping when the vacuum gauge reads about 25 inches of mercury.
Applications that would look into a long-term use of a GoPro have not occurred, and the reason would less be the vacuum conditions, and more likely the thermal loads and radiation. A standard GoPro assembly has nowhere to radiate heat in a vacuum and both the battery and camera itself would likely overheat during and near solar maximum and freeze during eclipse. The internal hardware in the camera would be easily damaged by single event upsets and would certainly fail over long (>3mo) periods of time.
That being said, I'm fairly confident that you could fly GoPros for short flights. I have personally flown Raspberry Pi Cameras and COTS Li-Ion batteries on sounding rocket flights to above 150km and successfully recorded video and operated instruments off the battery power. These flights lasted less than 20 minutes total.
Edit: This all being said, vacuum operation is not all that difficult to achieve. It's the other environments of space that are a concern.