Yes. However, I think it is genetic. My parents favored their left hand as children and were "converted" to being right handed. I can use my left hand for many things but don't write very well with my left hand. I had a friend who could write cursive with either hand and you could not tell where she switched hands in the middle of a sentence.
You can train yourself to do most things.. I broke my left wrist when I was in Kinder and had to do my work right-handed. I kept up the practice once my hand healed (my friends and I thought it was cool, since I was the only lefty in the class) and am now ambidextrous. I still practice my cursive (hardest thing to do), but it has come in handy many times.. Like when there isn't a pair of left-handed scissors lying around, or when I want to commit a crime.. Ha!!