100%. Steel doesn't just go bad, if it is kept dry so it doesn't rust it will literally last thousands of years. The desert is the perfect place for it, in the middle-east it's still fairly common to see guns left over from the mid 1800s still in use a hundred and fifty years later. And you're even overestimating the problem of barrel wear, it isn't typically dangerous, the barrel doesn't crack, the rifling just wears out eventually so your accuracy suffers. The main problem is the ammunition, which would definitely not be good after 400 years. Hell, ammo left over from WWII is likely to have gone bad, and that was less than one century ago. And you can't easily replace smokeless powder with black powder in most gun designs, it would work OK for single-shot or bolt-action guns, but nothing semi or fully automatic, plus it's a lot weaker too. That isn't really an issue though since smokeless powder is actually easier to make than black powder. Take a mix of nitric and sulphuric acid and dip cotton in it, boom, gunpowder. (Don't actually do this, because... well... boom)
I have no doubt that there would be a big pile of perfectly serviceable weapons in the bunker, they just don't have the ammunition for them. They in particular want nothing to do with the decayed who could make new ammo for them, since the decayed specifically target mutants to kill and eat.