If it's suicide then, yes. Really- when it's suicide, it should be obvious a person was suffering a lot. But- yes, because it would hopefully make people more empathetic and forgiving. Suicide causes other people grief. We know it will when we do it. I'd want people to understand it wasn't a flippant decision I made lightly. I wish more people would accept that a person goes ahead with it because their own pain had become greater than everything else.
Really, if it's natural death, I'd probably want the truth known too. I don't think it does any of us any favours to just pretend we're ok and everyone else is ok all the time. If people were more able to be honest, maybe more could be helped before things got so bad that they wanted to suicide.