Many freestylers and racers will tell you no. BUT a trails frame should do both quite easily. you'll want something with a 21 top tube, or maybe 21.25, and certainly no shorter than 13.65 on the chainstays. Most racing bikes seem to have chainstays longer than 14 inches.
I know a guy that regularly races a trails frame. And yeah you should be able to ride park and street on a trails frame just fine.