Yep. If you can get a recording of the "board mix" it'll be nice and crisp. That's not to say that you'd use the same mix that goes to the various house speaker systems but if you have one guy mixing the levels for live sound and then a second guy running a mix for digital recording (or even just a multitrack master for later mixing) then it can sound pretty damn good.

Plus you only hear the crowd cheering and yelling between songs or during a "sing along" segment when the audio engineer intentionally brings in the crowd mics. During the rest, you're only getting instruments and vocals, not Bubba asking Todd if he wants another beer.