Not necessarily. I've actually spent some time wearing a sword (long story that), and I often wore it the same side as the hand I drew it with, because I didn't want to have to move my shield out of the way to draw it. It's an odd looking maneuver, but you can perform it in very tight spaces. There are two ways I've done it, only one of which would work for that sword. Basically you invert your hand, grip the hilt (so that your thumb is on the side with the guard), draw up and forwards to the full extension of your arm, point the tip of the blade straight forward then rotate your arm so your arm is no longer inverted, then bring your arm, hand, and sword to where they're needed in your stance. It almost looks like a weird sort of flourish. You can draw a sword with just a bit more length than your arm like this.
This method was primarily used by Roman Legionaries because they had no room to draw a sword across their body in an extremely tight formation.
It is specifically intended for shield fighting as you cannot draw the sword into a guard effectively, but you can draw it without disrupting your shield arm.