NO, Everything happens shortly after the lynching, the investigation, the protecting of the G, the Gs whack, AND the gunblazing, Sabet was in line to be lynched, and GOT lynched, that Ze decided to gunblaze her just means its an infortunate waste. He does not get lynched because she was gunblazed, but that she is lynched first. As simple as that, nothing happens before the lynch, the nightphase where every action is taken into account happens AFTER the lynch, its not considered ngiht before the lynch. Hence the detectives action doesnt actually happen.
Now if we had lynched Ze by him having majority vote, that would meant Sabet would have been gunblazed. Only then.