I'm in two minds.
I think it's very important that they understand the power of social media, that what they say on here is forever, potentially, and that cruelty and bullying is amplified by online discourse. I also think that they may need to consider the potential life implications of things they say, if they are shared outside a locked entry later, or used against them. Basically, never to say something they wouldn't like their mother, their future mother-in-law, and future employer to read. It isn't like the spoken word. In addition, kids can bully adults. Teachers are human beings, and it's grossly unacceptable for them to be subjected to malice and taunts, just as it is other kids.
Having said that, I have had personal experience of a head who has tried to prevent any criticism of herself and her school, both via official channels (she refuses to engage at all - literally) and online. She does so even when the criticisms are both extremely serious and entirely, and provably, factual. She doesn't do so for any moral, noble or decent reason, but from pure self-interest. And that is where the freedom of speech aspect comes into play, IMO. In effect, she's trying to block whistleblowing. If something is bad, and important, and true, people should be able to voice it.
My child attended a school (Outstanding, laughably) which reported the parents of a little girl with high functioning autism to social services for Munchausens by Proxy without ever troubling to contact the diagnosing paediatricians - she has PDA, which is classically masked in school with the tension released at home. The history is horrifying - the lack of honesty, confidentiality and simple integrity displayed towards the family almost defies belief. In the same year, the school gave my (autistic, and bullied, both of which they denied when I tried to talk to them about my concerns) son 3s - exceeds expected levels - for his EYFS on self-awareness, and forming relationships. When my son left (because we found another local school where the class teacher drew us aside and asked if we'd ever heard of Aspergers within 15 minutes of meeting him, and suggested adjustments we could make) we emailed the head, asking for a meeting, and setting out our very grave concerns pertaining to the school's ability to identify and support children on the high functioning end of the spectrum. I was met with a staggeringly rude one paragraph reply which categorically refused to meet with us to discuss what had gone wrong, in order to help other children avoid a similar plight, and primarily expressed indignation that we hadn't left him there longer. I had explained in the letter that he was talking about taking his own life, at the time. Presumably the head wanted us to wait until he actually tried? 
I approached the head of special needs for the county, who was very supportive indeed, and then the local MP, which was a possible route suggested by the SEN head. The MP's senior caseworker described the head as "defensive and very angry" when she called me. Apparently their failing some of the most vulnerable children in their care was perfectly reasonable, and parents wanting them to approach the National Autistic Society for better training was grossly unreasonable and insulting.
A few months later, a letter was posted on the school's new website in the test area for the new webmistress. This letter was a confidential one the school had sent the paediatrician for the little girl I mentioned above, discussing their relationship with the parents. It had been up long enough that those parents had to contact not just the school governors to get it taken down, but Google to get it removed from the cache. Apparently, a letter that confidential had been left to float around the school system for over a year after the child had been removed, freely accessible to any staff member interested in reading it, and the training on confidentiality had been so abysmal that a staff member thought it a suitable sort of document to upload when testing hyperlink coding.
A parent on my Facebook posted a few months after that, because her daughter (aged five) had had her yoghurt explode over her packed lunch on a whole-day school trip, and the class teacher had told her that the ruined food wasn't her problem. She had been given nothing to eat all day. When the mum went in and asked to speak to the head, the head sent a message that she was too busy and it should be taken up with the class teacher.
I posted setting out my reasons for thinking the school an abysmal one, as above. I said I would not send any child of mine there, and I suggested she consider moving hers somewhere saner. I also suggested that she ask around, as there are other parents with horror stories which I couldn't personally relate, as I couldn't speak from personal knowledge.
This parent was called in the next school day to see the head, who was brandishing printouts, and told that she had to remove her post, that I had a personal vendetta against the school (apparently, going through the appropriate formal channels when the school failed my child so signally constitutes such in this woman's universe) and that I would be hearing from them. Three months later, and I am still waiting - perhaps she sought legal advice, and they informed her that truth is an absolute defence to libel, and furthermore it is arguably slander to tell people that someone with a legitimate and valid reason to complain about your conduct is instead activated by malice and pursuing a vendetta. Who knows.
Social media comments are, unsurprisingly, apparently on her radar. I have been told that the home/school agreement now seeks to control parental comments, firmly insisting that they follow the appropriate channels. But they block those channels, and then resent the people using them. I will say what I please about the place. Which isn't something I do often, having a life, but when my opinion is sought... I supply it. And it appals me that a parent with perfectly reasonable and justified annoyance should only have attracted the interest of this head when her own ego and reputation was suddenly involved.
This school, incidentally, is highly likely to get another Outstanding, given the head's expertise at staging, and employment of consultants to oversee her OFSTED-compatible leadership and management. You can't complain to OFSTED about a school your child no longer attends, and OFSTED don't deal with complaints about SEN provision at all. So OFSTED, as far as I am aware, don't know any of this has happened.