That's an interesting perspective. I disagree. I think if someone is tweeting about suicidal intentions then it follows that they are not concerned about the privacy of those intentions.
Many people don't understand the terms and conditions of social networks like twitter and facebook, and privacy with those services is ambiguous and difficult to manage.
If a person is feeling suicidal because the people in their life are not noticing their pain, I really doubt that knowing an algorithm had to do it will make them feel any better.
It'd probably be more successful if it had access to your IM/chat/email logs, where you're more likely to be emotionally revealing to people you're close to. That opens up a whole other can of worms re: privacy, though.
If a person is feeling suicidal because the people in their life are not noticing their pain, I really doubt that knowing an algorithm had to do it will make them feel any better.