Not necessarily. If we define the state as a territory's organized political community, then we need to bear in mind that at that time religion was considered an intensely political matter. Indeed, politics and religion were inextricably linked in the early modern period, not just in Europe but also in the American colonies. Had there been a strict separation between church and state in Salem, it's highly likely that the witch trials would still have gone ahead. Those responsible for government and the administration of justice would have shared much the same attitudes as the wider community. Indeed it's hard to imagine that anyone could possibly attain a position of authority in such a community without sharing a similar worldview to his fellow citizens.
One possible difference could've been in how the legal proceedings were conducted. A separation of church and state may well have allowed the investigation and prosecution of the alleged crimes to proceed on a more properly organized basis, but we can't be certain of this. Even if matters could've been conducted in a more orderly fashion, the fanatical conviction that Salem had a serious problem with witchcraft would still have remained. In such a toxic, hysterical environment, false accusations would still have abounded and lives would still have been destroyed.
In Reverend Hale, we see someone who recognizes the importance of justice. But given the very nature of the alleged criminal act involved, namely witchcraft, it's hard to see how this could ever be achieved. After all, how exactly can you prove the existence of witchcraft? Just about any strange behavior or outward mark or sign could be adduced as "evidence" in this regard.
This, then, is the fundamental problem. If a society believes, for whatever reason, that it is being undermined from within by a dark, malevolent force, then the question as to whether there should be a formal separation between church and state is largely academic.