Nope. The position and orientation are unrelated.
Having Z component in your forward vector means that you have some pitch in your rotation.
Forward vector with Z of +1.0 means that the X axis of the object (the front of the camera in your case) is pointing straight up while Z of -1.0 means it is facing straight down.
Position is irrelevant unless you are constantly tracking another object or point in space (in which case the camera will rotate as it moves)