Even if Acish was fooled, the other kings of the Philistines weren't. They knew David was dangerous. A wild animal on a leash is still a wild animal. Acish didn't understand that, and it was in David's best interest to make sure he didn't.
Would David have turned on the Philistines if he had gone to war with theim? I don't know; we can only knew what did happen, not what might have happened.