You can ask, but don't insist on it. Some families are connected on social media and it works for them. Some teens don't want their parents seeing everything on their pages (and will block you from seeing things, which kind of defeats the purpose of being friends). Following your teens online opens up a can of worms, and you'll have to figure out how to negotiate that new relationship.
Pain is an essential lesson for the emotional leap from childhood to adulthood. Mothers shouldn't be able to see photos in real time that capture their children when they're at their worst -- whether because of too much alcohol or too little happiness. We can, after all, sense when "something is not right," just from a photograph.