I think there is a difference between training to use your own weak side versus training to defend against or attack someone who is the opposite handed. If I'm right handed and I like to keep my power side back, do I train to also fight with my power side to the front (ie...'left handed') or do I focus on fighting from a single position, but I train to fight people who may be either 'right handed' or 'left handed'.
Maybe because I started in Taekwondo but I really don't tend to think about 'right handed' versus 'lefthanded'. Taekwondo sparring has techniques to work in open stance and techniques for closed stance and then ways of setting up a given stance. Given that some techniques I throw better with my right leg back some some with my left leg back, my mentality is more of trying to determine what strikes will be effective and getting into positiong to throw those strikes. In Taekwondo sparring, you don't really see a match with two people in the same position. There's constant shifting and changing stance to try to setup a given position or fake a given position to setup a technique, which may be thrown by the left or right side, depending on the given technique and given person.
So I tend not to think in terms of 'right handed' versus 'left handed' (and in fact I set up with my right side forward enough that I've had people ask me if I'm left handed, which I'm not)
Anyway, sorry for that wandering. I think it's important to train against an attacker who could be coming with either side forward, whether or not *you* train to fight only from your string side or try to train both sides (and i've heard arguments for both approaches) I think you need to consider that your opponent could be coming from either side.
One other thought is that there are some philosophies that have the strong side back and some that have the strong side forward, so even if you fight a right handed person, they may not be setup the way you like
Back to the original question, I don't think lefties have an inherent advantage in MA (I'm a bit of a bad one to ask because although I'm right handed I'm also a musician so I train my left hand to do more then most right-handed people probably do). I think some schools take an approach of being ambidextrous in everything at which point it may be easier for the left-handed person to do right side techniques then the reverse. However I've seen training that really only concentrates on fighting from one side, which I think is ok as long as you account for the fact that your opponent may be coming from either side. A lefthanded person who only trains to fight left-handed is going to be in the same position as a right-handed persons who only trains to fight right-handed. Keep in mind that if a left-handed person spends all their time training against right-handed opponents, they will be in the same predicament when facing a left-handed opponent as would a right-hande person; it's something they're not used to and may not have trained for.
So I don't think there's an inherent advantage, it just depends on how, and for what, you spend your time training....