yeah, and even then, to call Socrates a mouthpiece character means you probably didn't understand Plato. Plato uses Socrates to cause trouble at least as much as he does to express verbatim opinions. probably a lot, lot more.
the best way to understand Socrates, in Plato, is not to say "if Socrates said it, Plato meant it," but instead to ask "why is the sarcastic questioner who never means what he says attacking this particular line of reasoning?"
which brings us to the central premise: would Plato tweet? Plato wrote a book where Socrates explained that inventing writing was a dangerous thing which would destroy human memory. of course he would tweet. he would probably tweet that Socrates told him tweeting was a bad idea.