Is Social Media Commentary Next?

In a ruling that should catch the attention of all employees of state agencies, a federal appeals court upheld a ruling that former Georgia State psychologists didn't have a case against their employer over a memo they wrote critical of a policy change and reorganization of their student services clinic.  Inside Higher Ed's story has this key passage:

A district court found, and the appeals court affirmed, that the memo the psychologists wrote was "employee speech" related to their duties and thus not protected by the First Amendment.

Keep in mind, this was a memo to the employer.  Point being, if they'd decided they weren't getting a hearing internally and took to social media, would they have had more - or less -- First Amendment standing?