A: Short answer: NO.
A refrigerator, though it would seem like a logical place to keep your cigars, has a very low relative humidity. It’s usually somewhere around 42% RH, which is much lower than the 65% – 70% RH required for keeping your cigars moist. In other words, it won’t take long before your precious cigars are as dried-out as beef jerky.
Some experts say that odors from foods such as cold cuts, onions, Chinese takeout leftovers, etc. could possibly affect the flavor of your cigars. I’m not entirely in agreement with this, especially if the cigars are in cellos and kept in their factory box. However, getting back to the main point, your cigars shouldn’t be kept in the fridge in the first place.
For long term storage, invest in a cigar humidor. You can usually find good cigar humidors on sale, too. Your cigars will be much happier, plus, you’ll have more room in the fridge for beer.