In martial arts many exhale during any strike for maximum effect. There is a difference between exhaling and yelling or "kiai" in that exhaling serves a certain purpose (forcing oxygen into the bloodstream and muscles, causes a stronger core body for the strike to come from, timing, and a couple other things) where the yelling serves those purposes and a few more (makes you confident, suppose to make the opponent less confident, more releasing of energy and some other spiritual stuff). Most professional fighters (mma, boxing, wrestlers, est.) don't yell but do exhale which is why you always here boxers making those little wispy noises. Some go as far to wear swimming goggles and a snorkel during training to learn to exhale and inhale stronger. And trust me, you want to learn to exhale in martial arts, you never want to get punched in the chest or gut when you're inhaling... sucks hard.
But as for the benefits in dg... exhale through the throw. I hear a lot of people do it all the time... it may even be natural.