X pipe vs H pipe
Doesn't matter what the firing order is, unless you're firing two cylinders on the same bank one after another. And since no one does that, it doesn't matter.
The crossovers are far enough back in the system that it doesn't matter which header tube the exhaust pulse came from. Which, you could argue, means the scavenging theory is a bit of a stretch to begin with.
Regardless, the firing order of pretty much all the "V" engines I know fires a cylinder on the left bank followed by one on the right, or vice versa. Which means that adding a crossover will shorten the distance between pulses in the exhaust. I've seen a few car mag articles showing dyno changes with an X or H pipe vs no crossover. Most of them are pretty insignificant, usually just a few HP or couple of ft-lbs. Not anything you're going to feel on a butt dyno.
Most modern factory exhaust systems include some kind of crossover. If they did nothing at all, this would be a waste of money by the factory. Maybe its only a few cents per car, but more bends and more pipe equals more money. Since its not just one brand, and there are multiple performance cars out there that roll off the showroom floor with X pipes, I'm guessing there must be something to it. Even if its only because it sounds cool. Someone must think it helps to sell cars, otherwise you wouldn't see them in factory exhaust systems.