You could argue this both ways. I would tend to argue that things would have been no different if there had been separation of church and state.
From one point of view, you can argue that things would have been different. Witchcraft, in this view, is a religious crime. It was banned because the Bible said that witches should not be allowed to live. There is no rational basis for a ban on witchcraft. Therefore, this would not have been a crime if church and state were separate and the witch trials would not have happened.
In another view, however, there would have been no difference. In this view, people would still have been frightened of witches at this time and place even if the church did not control the government. Witchcraft could have been criminalized even without the church. It could have been defined as using magic to harm others. Things can be banned if they harm other people. You might think of this in connection with the issue of gay marriage today. We ban it in many states because some people think it would harm society. We do this even though we have separation of church and state and many people oppose gay marriage for religious reasons. Witchcraft could have been banned in the same way.
I tend to believe in the second argument here. If enough people believe a thing is wrong, they can usually get it banned even if their beliefs have a religious component.