It is impossible to transfer a torque across a hinge.
Unless something keeps the loose rudder from flopping freely, the worst can do is flutter itself off.
If the pushrod keeps the rudder in contact with the rest of the plane, then what happens to the airplane can be "odd".
Attached:
A sloper with ZERO, 2 and 3 vertical surfaces. As long as the speed is kept up, the version with NO vertical flies well.
Let the speed drop, and it can fly sideways and backwards..
The Kadet vertical was hit by another plane.. Kept the speed up, and landed straight ahead.