Only if it's the only cool dark place in your house
If there's one thing I've learned at my time at Extra Crispy, it's that Americans tend to refrigerate lots of things that you don't actually need to refrigerate. You can leave butter on the counter. Eggs aren't sold refrigerated in most countries. And a lot of the produce around your house doesn't need to be squired away in the crisper. Case in point: onions. Maybe, like me, you've made a habit of tucking the onions into a drawer in the fridge, in the hopes that the chilled air could prevent those suckers from sprouting and turning into unsavory mush. But it turns out that you don't need to refrigerate onions. And in fact, putting them in the fridge might make them go bad faster.
Per the National Onion Association (because of course that exists), onions last the longest "in a cool, dry, well ventilated place. Do not store whole onions in plastic bags. Lack of air movement will reduce their storage life." So that means they're just as happy stored in a drawer as in your refrigerator. The problem with the fridge is that the humid, cold environment makes onions go moldy and mushy quicker, and no one likes a mushy onion. Out of the fridge, onions can last for four to six weeks.
The caveat for all this reckless-seeming no-fridge onion policy is that it only works if your onion is still intact as a bulb in its flaky cocoon. Once you peel or cut an onion, the inner flesh is exposed and far less happy about being outside in the elements. Then, the National Onion Association notes, you should keep the onions in the fridge. Chopped or sliced, they'll keep in a sealed container below 40 degrees Fahrenheit for seven to ten days. And this is only about red or white onions, those that are in their bulb-like state. Green onions need to be in the fridge because they have a higher water content. Go forth, and know your onion.