The answer is almost certainly "not formally". The NSSF or NRA almost certainly has a social media monitoring agency that digitally scans a list of social media sites, including some fora, based an algorithms designed to elicit remarks on specific issues. I can't say what those issues necessarily are but based on other industries, legal and litigation issues, public policy issues, and "safety", however that is defined, will predominate. Competitive issues will be excluded to avoid any appearance of collusion or trust activities.
On a company basis, it is extremely unlikely that there is anyone tasked with specific social media responsibilities. I have a friend who has just taken up a social media marketing role with a major name brand firearms manufacturer and he was shocked and frustrated with the lack of attention and sophistication around social media. The firearms industry is o e of the more retrograde in that regard.
Having said that, there are gun guys and gals at gun makers. And in the more boutique manufacturers, accessorizers, and retailers, I bet there are quite a few surprisingly senior figures who do monitor and participate in social media relative to their industry, albeit frequently under alias.
So, the answer is "yes, but.." or " no, but" depending on your perspective.