It would not work for me.
I have tried the wandering about with two rifle cartridges suspended between the fingers of the left hand and find it so annoying that it is not worth the effort. But that would indeed be a left-hand load.
For me, and I own and shoot a lot of SxS's, rifle and shotgun, the right hand load is far more natural. Of course, I shoot many thousands of rounds more with a shotgun than a rifle. I break open the gun, maintain the left-hand hold, grab two rounds (rifle or shells) from the right hand pouch, pocket, or shell holder, drop them in the chambers, close the gun, and am ready to fire.
I should note, I also do a lot of driven bird shooting where I am carrying a shell bag. It is impossible to shoot naturally right-handed with a shell strap crossing the pocket of the right shoulder to suspend the bag on the left side.
The left hand drill could work on SxS rifles and shotguns that are assisted opening like the Boss, H&H, and especially the Beasley action used by Purdey. Often OU shotguns will wear in sufficiently for the barrels to drop under their own weight when the latch is moved to the right. That is rarely the case with the vast majority of SxS actions which are non-assisted - at least in my experience. However, when using a shell bag, one would still have the mounting issue.
A left-hand ammunition carry would be particularly onerous with a bolt action.