It is certainly possible to achieve straight asymetric
flight with level wings by use of rudder. As you say, this would involve the
aircraft slipping.
But why would this deflect the ball?
The wings (and therefore the instrument and the central portion of the
tube) are level.
The aircraft is not accelerating laterally, so the tube isn't being
snatched away sidewayds, leaving the ball deflected
by lagging behind.
The balls weight is acting towards the Earth, as per usual, and is
opposed by the ball being held up by the bottom edge of the central part of the
tube. Again, no unbalanced forces.
So there is no mechanism to cause the ball to be deflected, so it isn't.