We have one in addition to our own website; it's been a good way to get word out to parents about events, solicit volunteers and drive traffic to our own site. Just be careful to set it up so that only friends can post on your wall and see your details, and turn off ads because you can't control what shows up there and some of the images in ads are not very appropriate for a PTA/PTO page.
Our parent group has a Facebook page that has been in my estimation sucessful. It does require some organization tho. Yes, our superintendent and principal had to approve it. Our publicity chair submits what postings she wants to put up to the super and principal a week in advance to get approval. It may sound like a pain but all our other committes need to do the same for any email or flyer that they send home to parents so what's the difference. Sometimes they give us things they'd like us to put up on the page. They are also ok with us putting up non school event notices and articles that we think may be of interest to the families at our school. Hope that helps. I say go for it.
We have a facebook page for our PTO, we were not allowed to link it to the school's web page at all but are allowed to run it independently. We keep it to posts about upcoming PTO events, school events and things of that nature. I'm looking forward to it evolving more in the next year.