Nope, be it actually talking or sending messages, both are a no, sorry.
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You can do it on your phone. There's a playstation app, I forgot what it's called but just type in Playstation and it should show you the app's picture and it should show the PSN logo. For me, it works perfectly, and you can even manage your friends list, for ex. you can delete or friend a person, you could review the person's activity (doesn't work for me) [this is for all you stalkers out there], and you could even see what friends they have [ but the user you are viewing has control if they want to show you their friends or not]. You could also even make another name for yourself but it's not a username, instead it is like Kik. First, middle, and last name. For example, Walter White Suckslollipops. Something like that, yeah. And on the top left corner it includes the playstation store, once you press on it, it will direct to whatever browser you're using, like Google Chrome. Oh, and one more thing is that you could take a selfie of yourself and put it as your profile picture [ however, it will only be viewed by other users using the app, not ps3 users ] or you could put your app profile picture as one of those downloaded pictures, such as, you could put your profile pic as Batman. Hope this helps. (I wish there was a way to communicate to your psn friends on web :/ that would be REALLY helpful...HINTHINT. Hope that PSN sees this.)