I don't know how experienced you are at diving as nothing shows on your post so I did not look at your profile. Camera shooting or spearfishing both distract from safe buddy diving and to combine them sounds excessive. I have not done any spear hunting but I have screwed up horribly by following my camera alone. Additionally, having one mounted on a gun sounds like it could lead to entanglement challenges and at best loss of equipment when a camera breaks free. You just might get some video shot before the shaking on the line disrupts that, but I doubt you could get a good, clean shot.
Have you used either a speargun or a camera? Cameras don't shoot far away well; if you fire the camera first, the flash will spook the fish; if you fire the spear first, you'll be struggling with your target; and you don't get very good shots without a strobe anyway - which would really add to a gun challenge.
He is a very experienced diver. If he wouldn't, it's probly a bad idea.