The question should really be, "Did the elevator have ND authority during the period when the aircraft was on the wrong side of the stall warning?" The answer is yes it did, and indications are that it would have had control up to around 180 KCAS. If a Side Stick max ND command had been made and held for about 2 seconds, the THS would have started neutralizing the elevator demand. Any further ND would have provided increased control as THS followed and airspeed ramped up. The whole process could be sped up by use of the Manual Trim Wheel.
The only real problem I see in the way the THS operates is, the use of the Manual Trim Wheel appears to have been absent from the training regime, or at least discouraged. Why has this happened? The THS is a major control surface, and where it is positioned should be part of the instrument scan. OK, in Normal Law it is taken care of automatically, but in Alt Law the situation changes. Did the PF ever understand how the THS operated in Alt Law? We will never know, but if you don't understand a STALL WARNING, nor understand that consistently pulling the nose toward the heavens is not going to help you on this planet, then what chance does a trim wheel turning constantly for a minute within your periphial vision have of getting noticed.
As for the THS doing its 3°NU to 13.6°NU thing; it had nothing to do with 'autotrim'. It was operating in an integrated demand/time manner to neutralize the elevator input demand - nothing more. The elevator demand was wilful.
The A310 TAROM approach
zoom climb/stall/recovery incident at Orly on 24 September 1994 provides some insight into the movements of the THS. Though I note the PNF made some manual adjustment to the THS following the stall recovery while setting up for their second approach, and without the PF being advised. That doesn't mean that the PF was unaware that the THS was moved to provide better trim. Also, the incident was marked by NO stall warning, and the reason given was that AoA SW thresh-hold had not been reached before the IAS had dropped below 60 KTS and the control logic inhibited it. Sound familiar?
Essentially the same logic with minor changes has been around for a long time. Unfortunately it requires incidents/accidents before everyone realizes how some of this control logic works.