I suspect the answer would generally be "no", since there's generally not a lot of room in an ambulance, but you might be able to convince a police officer or fireman to take it.

I base this on my first accident, several years ago, when I collided with another cyclist, flipped over my handlebars and landed on the pavement, breaking my left collarbone. My condition wasn't too bad (i.e., I was sore and couldn't raise my left arm very high, but the skin wasn't broken), but it was clear I wouldn't be riding anywhere (in addition to my injuries, I'd bent the rear derailleur bracket). The police seemed to lose interest when I told them: a) there wasn't a car involved, b) I'd hit another cyclist (and was at least 50% to blame, c) I had no lock on me, and d) my car was 10+ miles away. The good news is that the fireman were happy to take it to the hospital in their truck as they were escorting the ambulance anyway. On top of that, the guard at the hospital took VERY good care of it, making sure to release it to my friend only after I'd given him the okay (I suspect he didn't have a lot to do).