I am not sure “quench” is the right description. I think in this example the barrel is just being cooled.
In metal working quenching is mostly done to harden steel, changing its microstructure by turning Pearlite into Martensite.
Most common steels need to be heated to around 1,500 °F. I use a magnet to tell when the steel has reached the Curie temperature or Curie point. At that temperature the steel’s permanent magnetism changes to induced magnetism and it will not be attracted by a magnet.
My point is you have to get the steel really hot before the structure changes and it can become brittle when quenched. I doubt that a couple of hundred rounds will generate enough heat to harden the barrel if it’s dunked in a stream. It will be hot enough to boil water and the stem makes a nice show, but it’s just being cooled, not quenched.
Here’s a M60 with a barrel that is probably hot enough to be damaged by quenching.
The bolt probably welded to the barrel. That’s what happened in Vietnam when guys kept linking belts, firing on very large numbers of enemy who were exposed and kept coming. Then they would do the same with the next one until it welded itself and the next…
As hot as that is, GE M134 Minigun barrels can get much hotter, past white hot to where they become translucent.
Back in the 60’s M134 barrels were good for 100,000 rounds. Now the Dillon Aero barrels don’t start erosion testing until 125,000 and most go to around 200,000 rounds. Metallurgy is always improving.
I don’t know what the life of GAU19 barrels is. It’s the M134’s big brother.
Electric guns are impressive, but I wonder if they can really take a strong EMP.