If you can run 13, you're good to go for the most part. Not many cars can do less than that except in perfect conditions.
A dragstrip is a specially prepared piece of asphalt and concrete. It's sticky as hell. The street isn't. You'd be lucky to find traction enough on the street to match your car's quoted 13 second quarters (a little dust here and there... boom... you're in the 14's).
Besides, most street races happen from a roll... that's if they actually occurred... and if it were actually permissible to discuss street racing here.
But considering we're talking about beating most cars on the road... last I looked, the average car does the quarter from 16 to 20+ seconds. Anyone who's got a 14 second or faster car can beat 'most anything'... and anyone with a 10 second car isn't actually going to do sub-10 second quarters without slicks and a track.
Hell... lots of guys here (Philippines) with 500-800 horses who can't break below 10's because we don't have dragstrips with enough grip. Very few people below 10, even with Hoosiers, tube-frames and fiberglass bodies... simply because there isn't enough grip to get hooked up for a 9 second run.