Yes words hurt whether or not you hear them in an ichat, over the phone, in a text, or in person. That's the key weapon of bullies- words. And while physical intimidation is part of it- they strike with words and destroy your confidence that way.
And I feel like the only way to get to them is to disallow them access on social media. People have enough to deal with online without worrying about someone making personal attacks on them. So as soon as that behavior appears, they need to be cutoff at the pass. And it shouldn't only be there but any network or site they violate policy.