I have done something similar by attaching a GoPro on my Aquatica housings for Canon 5D III and Sony MC50E eventhough I use the main camera for shooting video!
Benefits:
- The GoPro has a slightly wider angle of view so occasionally there might be better composition
- Whilst shooting continuously with GoPro, one might catch an event that otherwise might have been missed with the main camera
- I can film myself. For example in caves and wreck corridors you can get additional continuity and variety this way
- It is easier to take sneaky sideviews of accompanying divers
- The GoPro footage acts as additional insurance in case I manage to have a mishap focusing the main camera (see further below)
Drawbacks:
- One additional u/w casing to take care of. The GoPro is actually so cheap, that it is easy to become a bit complacent with it. I flooded one due to my own error
- The GoPro always runs out of battery before end of dive. My typical dive is 90-100 minutes in cold water.
- The image quality is not very good in low light and consequently the additional GoPro footage is rarely used
- Hundreds of GB of additional storage requirement.
- The hassle of charging additional batteries
Due to these drawbacks, I eventually gave up shooting with the add-on GoPro.
However, recently I really regretted this when I was the video shooter for an unknown submarine and I managed to shoot almost all of the footage slightly out of focus!