Yes—refrigerating unexposed film is generally safe even if the fridge has an air ionizer. Film is sensitive to light and to ionizing radiation, but a refrigerator air-ionizing feature is very unlikely to produce anything like X-rays or other radiation that would fog or damage film.

For storage, the bigger concerns are moisture and age. Unopened film in its original sealed packaging is usually well protected from humidity, and refrigeration helps slow deterioration. Once packaging is opened or compromised, film becomes more vulnerable to moisture and its shelf life is reduced.

So the practical advice is: keep the film sealed, store it in the fridge, and protect it from humidity. The ionizer itself is not likely to be a problem.