In my area a guy did similar to what you described but to railway station staff , didn't follow through with his threat and he was remanded in custody and was put before the court. and sentenced to two weeks in prison. Now there is a little more to it, as I know the guy ,he was in hospital same time as me and no doubt got fuck all help when he was discharged as well but personally If you are suicidal I don't believe in dragging other people into it as far as possible as why damage others?
And despite suffering with suicidal ideation,it wasn't admitting to suicidal thoughts and plans that got me admitted to psychiatric hospital ,in the UK at least the bar for an admission is higher than that,the mental health crisis is so bad here suicidal thoughts is shrugged off as there aren't the resources. It was actually my severe anxiety which I had to be medicated for by paramedics even before I went to hospital and no sleep for days that got me admitted. Despite hating hospitals ,I was in no fit state to argue with them,just lay down and agreed to it.