The mental toughness that you have expressed while training for four of five months will mentally and emotionally prepare you to run that final mile of a half marathon or the final hour of a marathon.
I would rather have runners invest that extra energy in their one speedwork session each week.
If a runner is still concerned about completing the entire 13.1 or 26.2 mile distance before the event, I often encourage them to drive the course before their big day. If the race is a local event, runners can also do several of their long training runs along portions of the course. This will familiarize themselves with the terrain, opportunities for crowd support and scenery.