they will at first, when you first draw it in. but if you had passed science class, you would know that water has a higher specific gravity, and it will sit at the bottom. so all you would end up doing, is injecting a bit of water, and then injecting oil. but still leaving a bit of oil left over, that you were worried about in the first place.
so as big said, use a small bubble of air. thats pretty standard injection technique.