This is not correct. When the system is in alternate law the auto trim function is disabled. Pushing the stick forward only results in limited elevator motion. Trim must be addressed by the pilot in this mode, so simply pushing the nose down isn’t going to retrim, the pilot has to do it manually.
Yes, while in alternate law (and with the AA over 40º, abnormal attitude law) auto-trim is disabled. However my comment was in regard to the scenario Yipoyan referred to with the Chinese A300 Go-Around. In this instance, had a nose down input recovered the stall, and thus normal law returned, the auto-trim would have moved nose down.