Is it acceptable to reach the short-time stall warning during automatic go around with one engine inoperative? Should I disengage AP and proceed manual go around?
Please explain this a bit further...as you stated you are on an automatic go-around...you mean a coded procedure? What is the aircraft type?
As this is not a typical scenario, am I to assume this is a sim?
Here is the issue with a coded procedure...
The procedure is based on many factors, typically a combination of many factors. EO performance is very, very limited on a twin...while the procedure may work in design, in the sim, depending on the settings, it may disco...on the flight val, there are many issues that come into play.
The flaps settings may not change as fast as the procedure design required, for the most part, it is the initiation of the EO missed approach...
The EO missed, assumes the worst case, EO at the MAPt...in reality, if you are EO, at the MAPt (you better be going in) if we look past the worst case, initiating the missed before the MAPt, with some energy other that the final approach speed, then this is much more of a real time situation.
Aside from that, your individual aircraft, and the particular box, from Honeywell, Smiths, or others, will have their own particular settings. Some boxes will give you a prox warning on the missed, assuming a 400' ROC...others will not...
If you were to provide more details on the aircraft, box, altitude, sim, etc, it would be easier to determine...
(stall warnings are never good, no matter who makes the box, but it happens in low speed transitions) what to do is another matter.