§ 11.432 Impersonating a public servant.
A person commits a misdemeanor if he or she falsely pretends to hold a position in the public service with purpose to induce another to submit to such pretended official authority or otherwise to act in reliance upon that pretense to his or her prejudice.
That wouldn’t hold up in this case, because of that very important word “purpose”. They weren’t trying to get anything due to authority. In fact they were trying to make sure that Facebook was only approving ads by the actual authority.
Which is what I think parent was pointing out. Even if they ran ads saying "vote for me", it probably wouldn't fall under that language. They'd have to be inducing action in their official capacity, not as a candidate.