My 14 year old son has been a competitive swimmer since he was 7. He quit swimming this year mostly because he just got tired of it and to swim competitively in high school requires so much time he wanted to devote to other things. This is what I can tell you about how swimming helped him.
He has never had shoulder problems in spite of all of the ball he plays. He did suffer minor LL elbow when he was 11 though.
He was always in top physical condition with respect to strength and endurance. He was definately more disciplined than any of the other boys his age no matter what other sport he was involved with.
The conditioning that swimmers undergo is in my oppinion quite extreme and is definately not for everybody. They swam as 8 to 11 year olds 2,500 to 4,000 yards per day, 5 days a week. As a 12 to 14 year old, he swam 4,000 to 6,000 yards per day, 5 to 6 days per week. During the summer he would be in the pool at 7:00 am and 3:00 pm (when baseball didn't interfear) for two-a-days. He would compete in a meet about once a month not including LSCs. He never quailified for a Zone meet. (It's funny in that he thinks swimming is a sissy sport that baseball and football players don't do. Remember, he is 14 year old and knows everything. LOL.)
Other then the overall conditioning that swimming provides, the best crossover benefit to overhand sports are going to come from the butterfly stroke. This is a difficult stroke to learn to perform properly and is very high intensity and requires a high base level of conditioning to do and learn. The butterfly arm motion is very similar to overhand throwing and almost indentically incorporates the same muscles firing in the same order when done properly. Here's the rub, to learn good technique for this stroke almost certainly requires the instruction of a qualified coach and a focused effort on the part of the swimmer over time. It is considered the second hardest stroke to perfect behind the breast stroke but, it definately is the most physically exhausting.
Unless you have the time and determination to achieve the conditioning and the technique, I recommend that you use swimming for the excellent overall conditioning it provides. Swimming has a very low risk of injury. It is a constant light resistance void of the pounding and joint stress that runners endur.