It depends on many factors.
The act of charging takes energy, so the GoPro may well turn its charging circuit off once has charged the internal battery, then the Powercore then sees a long enough time without draw then turns itself off.
What @bobbleheaderman is thinking may actually work best, remove the GoPro's internal battery so it constantly draws from the Powercore which then keeps output.
The math will need checking with a test. The electronics in the Powercore is doing work and even if low level of work, the fact the electronics inside the Powercore is running for hours, is taking some of the energy away before the GoPro sees it.
I'm saying just don't assume anything. Oh and a bigger battery would be more viable.
Don't need the fastest / expensive, just lots of mah.