The A/P on the 737 will disconnect , once you press the TO/GA buttons
And that depends on system status and SOPs. If you always use a dual channel approach, as some carriers do, then no, the autopilot will not disconnect and fly a nice and easy automatic go around with reduced thrust, as long as you press that TOGA button only once. Even in manual flight, if using the AT ARM mode (SPD deselect), reduced go around thrust will be set on the first click, and not more. Of course, it has the downside of the uptrim at around 380ft AGL, but that is a non-issue if trained for it.