It's a decision that needs to be considered carefully. However, I think the odds of survival favor a guy with a gun and no training vs a guy with firearms training and no firearm! Training is important and a big asset but many untrained people have used handguns successfully for self defense. As Mark Moritz used to say the first rule of gunfighting is have a gun!

That said, as long as you know how to use the shotgun it's a fine home defense tool, probably better overall than a sidearm.