By a matter of genetics, yes. However, most knights of any era trained enough to be at least moderately ambidexterous.
If you are a fellow southpaw thinking about supporting a request to learn kenjitsu or Iaido left handed, forget it. Today's Japanese schools stress tradition too much (especially Iaido), and the righties' main objection is simple and seemingly straightforward: the instructor can't show you exactly what to do because it's backwards.
Now, we lefties understand that, for us, mirroring actions is as natural as doing them straight. However, I've argued that before with Charles, and gotten nowhere. So, my advice: come over to the light. Start fencing.
Fencing Club at UH