Ben,
When someone doesn't know something, and they want to know, but they don't ask, that is stupid.
I don't have formal Judo training, but I do know a handful of Judo takedowns/throws. The thing is, once you have already gotten out of the line of fire, and you have some control on the gun, there are lots of good options from various MA systems, and I can definitely see some Judo stuff potentially coming into play ( maybe a little modified to make sure the gun does not point at you while disarming ).
It should be noted that with a semi-auto pistol and a revolver, there are places to grip the gun so that it cannot be fired. Even when you do something like this, it is advisable to never let the gun point at your body. Due to the nature of the Fickled Finger of Fate.
The big question is, how does a Judo man
close the distance safely, so that he can apply his techniques. In traditional Judo training, there is no answer to that. Though you will probably find some police forces that use Judo, will likely have a few strategies for this.
Out of all the gun disarms I have seen taught, I think I liked Bill Kipp's, and Marc Denny's approaches the most ( for my own personal way of doing stuff ). Not really any Judo there though.
When considering my responses in a high-risk-of-death-situation like a gun attack, I often ask myself this.
Do I want to trust a style, or simply trust myself ?
It's not about dismissing styles, but about creating the correct mindset.