does the nailgun benefit from supports shotgun damage/pen benefits?

I have a level 25 support class, I want to level up my berserker a bit, as it's level zero now, so I was thinking of running with the nailgun on my support class as the nailgun is classified as a shotgun. At least until I my berserker up to level 5 or so. But I'm not sure if the nailgun gains the shotgun benefits because it's not a support weapon, so I'm not sure if it's worth it. This has probably been asked before, but does anyone know if the support benefits apply?

does the nailgun benefit from supports shotgun damage/pen benefits?