The answer is No. And Yes.
Yes, we know that this is a confusing answer but it depends on the environment where the olive oil is routinely used.
Olive oil, but we mean extra virgin olive oil have to be kept in a nice dark cool area. Light, hot, air and moisture are the enemies of olive oil, and the longer the oil is exposed to such factors, the quicker it would go rotten.
By putting it in a dark cool area, you can expect to have it about a year, or even 2 years shelf life (though it does get worse with each bottle opening). That’s also why all the best olive oils are kept in dark bottles or metal cans. The closest you can get the temperature around the oil to 14 C the better, as this is the ideal temp to store the oil.
Now, if you have to keep your olive oil in a warm place, such as in a busy kitchen or in a non-air conditioned kitchen or in hot areas, then there may not be a cool enough place in your kitchen to protect it best. In these cases (and only in these cases and there is no cool enough area), then it actually might be a good idea to put it in your fridge. As long as the fridge is well ventilated and your bottle or can is well secured and closed from further air exposure, the oil will get cloudy (as the fats start to coalesce).
The problem is that as you can see, that olive oil can't be used until it returns to room temperature. Also, long time refrigeration and rewarming can put a bit of strain on the oil, which will degrade the flavor faster. But, if you're in a hot region, and the other option is distorted oil, then it's better than wasting the oil.
Another nifty trick though to preserve your olive oil is in a cooking trick. You'd be ditching the bottle all together as you'd be freezing your olive oil in ice cube trays.
We tried to keep "olive oil ice cubes" in our freezer with frozen herbs inside them. It's a quick way to use these cubes for recipes like stews, crock-pot recipes, braising and such. You'd be really surprised how much extra flavor a cube can give.