Well, lots of people do it on a road bike, I'm sure. If it's your only bike, do you have a choice? It's one of 3 options:

1. Do it on your road bike
2. Don't do it at all
3. Get a hybrid, cross, or mountain bike and do it

I suppose #3 is out of the question. And you'd like to do #1, instead of #2. And many people do #1. So, it's probably safe to do #1. I bet the worst that could happen is you get a flat on the road, or need to true your rear wheel.