I’m inclined to say, it would make them less likely to panic, and that’s about it.
Most self defense training should hammer home the idea that you do not want to go toe to toe against someone with a gun.
If they have a gun, and that’s your question, it’s not really going to help them at all. There’s no overlap between firearms handling and what you’d get in most self defense classes.
The same should be true of sport and competition martial artists, though, it is possible a sport fighter would think they’re good enough to take on someone with a gun. They may also have had training in some of the disarm techniques. I’ve heard of a few cases where this did happen, and none of them ended happily.
Again, they’re not going to have any advantage in handling a firearm from their martial arts background.
Of course, it’s always possible someone does have a history of sport shooting, which might help them when you put them in combat, (or get them killed, it goes both ways).