Lets be honest, the ''''massacre'''' itself had a total casualty count of 5 death and six injuries; black friday is deadlier
It is not the death that really pushed the ARW but the culmination of years and years of percived abuses from the British crown. Unless the British allow the soldiers to be trialed by an american court (which wont happen, it would be a military court) the revolutionnary would inflate the story to win public opinion.
They were tried by an American court, that's the whole point. The colonial government realized it was in some deep shit after their soldiers opened fire on a crowd of civilians so they opted for a fair trial to look better, and they even got John Adams to handle the soldiers' defense in court. He managed to get most of them acquitted, and two were convicted merely of manslaughter and punished by having their thumbs branded. If the defense was more incompetent and/or perhaps even represented by a loyalist rather than a prominent patriot like John Adams (therefore making the case out to be much more impartial) the court might very well find some or all of the soldiers guilty of murder and sentenced to death.
As for public opinion, the trial was more of a sideshow to that, public opinion in the colonies was already generally of the position that the British conducted a massacre of American civilians in an attempt to suppress their liberties. The total count of dead was well known but "merely" having five people die was not enough to wash away the anger towards the crown. If anything the executions of some of the guilty soldiers might actually assuage colonial resentment. As for the cause in general though, too much has already happened to stop the road to revolution and I don't see the British being more lenient after some of their soldiers have been executed.