In all Boeings go-arounds are initiated manually though you can engage A/P soon after.
It can be, but it doesn't have to be. If we fly a autoflight ILS it is always dual channel and therefore the go around is flown by the autopilot. Of course one could argue that it is initiated manually by manually pressing the TOGA switches. Automatic go around while nice is not the main reason for dual channel approaches though, it is a fix for some very nasty aileron hardovers flown by one faulty autopilot on one of our early classics, dual channel approaches will prevent that.
However, if already in manual flight that is of course a moot point, still not a difficult procedure if the training department does now how to do its job.