Not even. I don't use purchasables. I don't worry about other players having them. Sure they can be strong but you can buy armor. The spawn weapons are plenty good at downing enemies. By the way, I have noticed that if you spot someone with a shotgun your character yells 'shotgun' or something like that. This helps you evaluate the situation and stay back.
If they're wielding the Shotgun at the moment, yes, it's called out. If not, it won't be called out. They also won't be called out if they're using Covert Training 3. Makes for some rather amusing moments when you run into them the first time in Survivors (I suppose Supply Raid would aslo apply), then later facepalm-worthy ones when you run into them again and rush them without checking their nametag. (This happens to me a lot more than I'd care to admit. >.>)
Armor helps against the Shotgun, but just a bit. It fires surprisingly quickly despite it being pump-action. I swear it fires faster than the Semi-Auto Rifle, destroying your armor and then you in a split second. lol Armor, last I checked, doesn't protect your legs either. In other words, if you're in close range to a Shotgun user, you're screwed. It's the undisputed king of its effective range. You'll stand a chance against every other weapon in their range or even close range as you get a little time to react.