100% correct!
I have participated in research and development tests where we had to fire weapons at precise amount of milliseconds between shots. A fire control system using computer controlled mechanical actuators would fire the machine mounted weapons. These shots where filmed at 10,000 frames per second and higher video. Despite a room full of electrical and mechanical engineers, we had to "dial in" the timing for the exact delay by observing the delay between shots. There are a lot of variables for this.
Obtaining a double discharge where both barrels reached peak pressure at the same time is difficult in a laboratory, and darn near impossible in the field.
Interesting to know. And as a gesture to @Paul Homsy who thinks I was being obtuse, I do see a way to put a formula to his assertion of 4x pressure in a true, flawless double discharge.
I took a 470NE at 2150fps using 106gr charge, a 500gr projectile, and an 11lb gun. If I assumed the bullet is then 1000gr and the powder is 212gr and the velocity is still 2150fps and the gun is still 11lbs, that math outputs not 74ft pounds of recoil, but 296 Ft pounds.
No idea if that math is correct and as you point out, no idea if a real world doubling would have a similar effect.