Yeah, I would try it. In fact, I think it is the best way to fight a southpaw. What you are doing is gaining the inside punching position, which is the most advantageous position. In this case you are getting your left hand inside both of his hands. By jumping to the right, like in the video, you take yourself out of position entirely.
So if your left foot is inside his right foot, your jab is inside his jab, a better angle. His body is vulnerable to short left hooks and uppercuts, and his liver is right there. OK, so you have moved 'into' his left hand but you know that and you know he wants to throw it...And your left hand is in perfect position to beat his to the punch (traveling a much shorter distance, and him moving to it with the force of his punch). You are slipping to your right, with your right hand to block or parry his left, and hooking or jabbing.