Yes.  The theory that government employees shall relinquish their First Am. rights they would otherwise enjoy as citizens to comment on matters of public interest [the “right-privilege” doctrine] has been unequivocally rejected.  Instead, the  government employer can only prohibit an employee from speech on an issue of “public concern” if the employer’s interest outweighs the employee’s in the following test: “The interests of the [government employee], as a citizen, in commenting upon matters of public concern balanced against the interest of the State, as an employer, in promoting the efficiency of the public services it performs through its employees.”   The Court found that P’s expression involved no impairment of the ability of superiors to maintain discipline nor did it pose any threat of disharmony among co-workers.  P’s employment relationships with D  did not involve “the kind of close working relationship for which it can persuasively be claimed that personal loyalty and confidence are necessary to their [the relationships’] proper functioning.”  Thus, the employer’s interest did not outweigh the employee’s, and P had a constitutional right to say what he said—to the extent it was correct—without being fired.  But the Court pointed
out that if P had used “inside info.” or criticized his direct supervisor, then there might be a breach of efficiency and he could be fired.  This is so even if employee’s speech were true.1.  Dave cites the Secretary of State criticizing the U.S. President as an example of speech that could be prohibited since, even though it is true, it interferes with the efficiency of the President’s
foreign policy.
b.  Some of P’s statements were found to be false.  In the event that
a government employee’s speech is false AND is about an issue of
public concern, then the New York Times v. Sullivan “actual malice”
standard will apply.  If this standard is met, then P can be fired
and held liable for dams, but if it is not, then he cannot be.  Here,
P claimed that the school spent more on athletics than it really had.
The Court held that D had not presented sufficient evidence to show
that P had acted with “actual malice” when he made these statements.
Thus, he cannot be dismissed or sued for his statements.