First up before I say anything else - speak to your doctor/physio/surgeon before you go hell for leather into any training routine while you're injured. The last thing you want to do it prolong your recovery or worsen your existing injury. Also, there are times when giving your body a break for at least a couple of weeks might actually be the best thing for it. Speak to your doctor, assess your situation and make your decision.
Training when you're injured can have a lot of benefits if you do it safely; it can slow muscle atrophy if you have limb immobilied, maintain your existing fitness levels, or at least prevent them from dropping too far, and can lessen the psychological impacts of injury. Unfortunately if you're injured and want to stay active, you may have to accept that you won't be dancing for a while. This doesn't mean you can't work on specific aspects of technique or fitness, just be smart about it. Any time I've injured myself I've found boredom and frustration can be one of the worst aspects so finding a way to stay motivated and at least maintain a basic level of activity feels better than nothing.