A guy is on the platform and decides to jump onto the line below him. Will he be electricuted straight away?
No, otherwise the trackworker fatality statistics would be through the roof. You need to be completing a circuit, i.e. providing a path to earth, to receive an electric shock. Touching the conductor rail and the running rail, or anything else conductive is a good way to do this.
In certain circumstances you can deal with the live conductor rail using insulated tools. Opening hook switches and applying test lamps ("box of eggs", used to see if the rail is live or not) are examples of this, a hook switch pole being made of wood wrapped in insulating tape and the test lamps being a wooden box with a running rail clip to provide a safe path to earth. A bit disconcerting when putting the eggs on and you get some nice sparking.
You will not die, or be injured, just from being on an electrified line. However, unless you know what you are doing and which parts are live, it's risky being on or near it.