He'd be handing the ball off to running backs with the other hand, right? And when he threw a pass, the ball would spin in the opposite direction. Fumbles and dropped passes...
I was a WR back in the day. The “opposite spin” is something you figure out in passing drills in the first 5 minutes. I wouldn’t think the RB’s would have any trouble with it either. We had a lefty underclass QB replace a senior midway thru the season. He threw a sweet ball. Ended up with a full-ride to Florida.
Switching back n forth in a game? Maybe there is an adjustment. But no more than the usual throwing touch.