Sure can! If it gets inside the fan motor you're likely to cause shorting, or at the very least corrosion, both of which aren't good if you want the fan to keep working. I wouldn't say it's "dangerous" per se if it's only running off a couple small batteries, more just that you're likely to ruin the fan.
Can I ask why you want to spray water on a running fan? Are you trying to make a mist device thingy, like something to cool a person off?