You're correct, the ice block will not turn automatically. It will require a torque. In aviation this is basically what is called coordinating a turn. With an airplane, if the pilot does not provide the necessary coordinating torque via rudder/elevator inputs, the torque will be generated automatically via the weathervane effect, which tends to align the fuselage with the velocity. So, you can effectively turn just by banking, if you're not anal about keeping your altitude and airspeed constant. In a helicopter, it's a different story, as the helicopter doesn't have much of a weathervane effect at least at low speeds. With a helicopter at low airspeed if you just bank without coordinating rudder then you just slide sideways.
The way the ball can be off-center is if the relative wind is off-center in the yaw axis.
The plane has a rudder on the vertical tail fin, and it is connected to pedals where you rest your feet.
If you press forward with your right foot, that pulls the rudder to the right, causing the wind to push the tail to the left, and the nose of the plane swings to the right.
This does not change the plane's direction of motion, only its attitude relative to that direction of motion.
Because the wind is hitting the left side of the plane,
you feel it immediately as a sideways force - your shoulder presses against the door, and the ball moves off-center.
The thing about turns is, in the process of entering a right turn, say, you must lift the left wing, by depressing the aileron on that wing.
That not only lifts the left wing, it drags the nose to the left.
The aileron on the opposite wing also drags, but much less.
This aileron drag is called "adverse yaw".
To counteract the adverse yaw, you can apply some right rudder.
When you've done that properly, the ball stays in the center, and that's called a "coordinated turn".
Of course, once you're in the turn, you don't need to bank further, so you can relax both the ailerons and the rudder.
When you've reached your desired heading and want to straighten out again, you do the opposite.
It takes a bit of practice, and feels great when you do it right.
The other use for the rudder is in a cross-wind landing.
As you approach the runway, you are "crabbed" sideways because your nose is facing the relative wind.
If you landed that way, you'd trip over your wheels, so before you land you rudder your nose into alignment with the runway (incidentally producing that sideways force).
To keep the sideways force, and the wind, from carrying you off the centerline of the runway, you bank into the wind, effectively turning into the wind at the same time as you are uncoordinated.
Since you are banked, the lower wheel touches first.
With practice, and if the wind is steady enough, you can travel the entire length of the runway on one wheel and then take off again.
EDIT: Here's a little picture that might make it clear why pressing a rudder pedal would make you feel a lateral acceleration:
Best Answer
In short, you are right, the pendulum has an angle with respect to the gravity vector, but your reference frame has this same angle, making them aligned.
A 1-G coordinated turn is a turn such that the horizontal component of the lift is equal and opposite to the force generated by centrifugal acceleration. E.g like this:
Obtained from Free online pilot ground school
The pendulum will experience the same acceleration as the aircraft, thus gravity and centrifugal acceleration.
It all depends on the reference frame, since this defines what you see as down, and sideways.
An external observer, which defines down in the direction of the gravity vector, will say that there is an angle between the pendulum and the 'down'-direction.
If you are on the plane, and you define down as the place place where your feet are (thus in the opposite direction of the lift), you will see that the pendulum aligns with your feet, and thus there will be no angle between 'down' and the pendulum.