No, the observation of quantum tunneling of a grain of sand through a sheet of paper would not falsify the claim of non-zero probability in quantum mechanics for such an event. In fact, quantum tunneling is a well-established phenomenon predicted by quantum mechanics and has been experimentally observed in various systems.
Quantum tunneling refers to the phenomenon where a particle can pass through a potential barrier even though it does not have enough energy to overcome the barrier classically. In classical physics, the particle would be completely blocked by the barrier. However, according to quantum mechanics, there is a finite probability for the particle to "tunnel" through the barrier and appear on the other side.
The probabilities associated with quantum tunneling are calculated using mathematical models based on quantum mechanics. These models have been extensively tested and have provided accurate predictions for a wide range of quantum phenomena. Numerous experiments have confirmed the existence of quantum tunneling in different physical systems, such as electron tunneling in solid-state devices and alpha decay in nuclear physics.
Therefore, if an observation were made of a grain of sand tunneling through a sheet of paper, it would actually be consistent with the principles of quantum mechanics and not contradict the claim of non-zero probability for such events. It would serve as further evidence for the validity of quantum mechanics in describing the behavior of particles at the microscopic level.