I believe the go-around button is designed for use on a coupled instrument approach when your approach speed is probably in the 90 - 120 kts band. It will only change the attitude to obtain 75kts. There is no collective input on the SFIM auto-pilot to add power to make the climb.
IMHO, I dont believe that given the low altitude/extreme unusual attitude, that the go-around button would have made any difference.
Most of us that have flown off-shore at night on inter-platform shuttles will recognise these conditions and will know how quickly you can get into the s***. RIP