Many artists who sing and play guitar will go to dummy chord voicings that facilitate easier playing in alive performance. Often times you'll see a side quitarist (or two) on the side accompanying.
But some guys (Dave Matthews, James Hetfield, and John Mayer) can handle the guitar by themself, play the studio cut album version, and still sing.
Those guys are performers of the highest caliber.
For me, I'm always humming, singing, or beatboxing while playing. You just need more practice and experience.