If a "depressed" person is posting things that flag a SUICIDE watch app, then I'd say they are obviously posting those things to draw attention to their issues. Therefore someone noticing would probably be just what they want.
Twitter feeds move pretty fast. People might not notice a cry for help until it's too late.
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.
My friend posted a 'suicide note' on MySpace back in the day. He was a funny guy and everyone thought it was a joke about drinking too much. It wasn't.