As far as I know, the aircraft will go around even in CAT1 FMA display condition.
i.e. if you only have one autopilot engaged it will still go around on the selected autopilot as long as the PF selects the thrust levers to TOGA.
It seems to be no different to a go around from a non precision approach in my mind, however I stand to be corrected.
In fact I believe if you were on fire, with one autopilot operative, below minima and you elected to continue an ILS on one autopilot, as long as you get LAND GREEN by 350' the aircraft would land happily. But, it wouldn't have been your day.