US soldiers fighting in the Philippines at the turn of the 20th century did this. Dunno how effective it was but the US won that war.
The most effective way of defeating Islamic terrorism is for the Islamic communities themselves to stop it. The majority of muslims, like the majority of most people, just want to get on with their lives and not face lots of hostility. Radical muslims who want to kill infidels are a minority. But in between those and the ones who are entirely peaceful, are those who would never do such things but are willing to turn a blind eye because it's a cousin or a schoolfriend or, simply, because they sympathise. The West has indeed done terrible things in the Middle East and many muslims are closer to the victims, see the photographs that our press don't run, etc. It's not enough for them to commit murder, but they understand those who do. And so Radical Islam incubates rather than is challenged and thrown out. Tactics such as suggested above achieve the opposite of what is needed. They heighten the division making it "West vs. Muslims" which is obviously less helpful than "West + Most Muslims vs. Radical Minority."
Again, our best weapon in defeating terror are muslim community members themselves who know when their neighbour or cousin is going off the deep-end and are willing to stop them. No amount of surveillance can match that. So massive affronts to their beliefs only weaken our ability to anticipate attacks like this.