No, it does not (unless you're in PR business where having the activity in social media is a "criteria").
Your social media is usually part of your personal life, which is best kept separate from you official one. So, your activity (or lack thereof) has no impact on your employability.
However, one point to mention, using social media networks or other forums which are meant for professionals and job search, (like StackOverflow careers, LinkedIn etc.) can have a positive effect on staying up to date about the offers and job postings, however, that does not mean you have to be ""active", you can be a passive researcher and only use the platform to connect to potential employers.
Remember, this will only help you in awareness / info about jobs/open positions. It's likely to have minimal to no impact in the interview and hiring process, though.