I would guess so and a lot of them have fled to places like Lebanon, America, etc. However, they shouldn't have to. Those who claim to call themselves followers of Y-shua should be defending these "Living stones" against persecution. If they all flee, the holy sites, like the Church of the Nativity will become museums.
I hear a lot of talk about defending Israel, which is wonderful, but I hear next to nothing from those who claim to belong to Y-shua about their bretheren over there stuck in the middle of this terrible situation.
No, these places will all become mosques.