Yes, you can play into the guitar input and use the effects and sing through a mic into an input at the same time if you want while hearing the drums without recording them. In fact, the drums play on their own track as if being driven by midi until such time as you bounce them to one of the recording tracks which you have to do if you want to take the tracks out to a software DAW.
I put up some a song I did with the BR-600 on my SoundClick page. I used the on board drums, the bass simulator, and the guitars and vocals were all recorded with the on board mics (though I ran the tracks through Sound Forge noise reduction before mixing.)
Look for "Your Eyes" at:
www.soundclick.com/danphilgreen
(you will have to scroll to the bottom of the song list)