The simple answer to this question is no - running/dancing/exercising on an ankle injury is not typically recommended.  Some injuries are minor enough that you can continue on your normal daily activities outside of exercise, but immediately returning to demanding and high-impact activities (or even returning within a week of an injury) can do a lot more harm than good.  Generally speaking, there are alternative exercises that can help you to keep fit while you recover and these include any upper body workouts and core exercises.  Dancing, running, biking and other lower body workouts (while frustrating to stop) will lengthen your recovery time after an ankle sprain.  The better you are at taking time out to heal early on - the sooner you will be back to your regular routine without pain!