Well, being a southpaw can give an element of suprise! Some boxers of an orthodox stance (those who arent southpaw) learn to box southpaw as well in order to quickly make a change to suprise the opponenet. A quick change could put the opponent back a second or so. While this may not seem like much, it is enough to shock an opponent and get a punch or two in. This fact is well known to boxers and was employed to world-record effect on Nov. 4th 1947 when Mike Collins, a natural left-hander, emerged from his corner in a right-handed stance before suddenly shifting left and delivering the fight's first and last punch, knocking out opponent Pat Brownson in 4 seconds.
On a more personal note, I used to do Karate. I am left-handed. I know that karate sparring and competition is much different as we use kicks as well as punches but the fact that being a southpaw is unexpected is the same. My brother (also southpaw) and I both were taught as right-handers like the others, and always had to do twice as many reps. on the left had side. I believe that while this wasnt the best thing, it was still good. I fought from a right-hand/orthodox stance usually but did switch from time to time. The opponent would often be shocked and I could get in a fair few good hits.
If you are quick, you can get in huge hits while changing stance. Starting from the orthodox stance, your opponent becomes open when you switch. A large portion of skin, often under hte heart (one of the best target areas) is exposed!
Good luck! Email me with any questions