The area of deflection would likely be very large and gravity would still be normal to the surface of the water, so no, you probably wouldn't be able to tell. You might perhaps notice the horizon being closer.
In orbit only the center of mass of the object is in free fall.
Anything farther away is falling "up" and anything closer is falling "down". So the water would fall "down" (i.e. toward the moon).
But since there is plenty of gravity on earth this would mean the water is effectively just lighter. And water on the other side of the Earth is heaver, and would flow to the lighter area until the lighter side was tall enough (i.e. had enough extra water) to balance that out.
