From page 472 of the Pathfinder Core Rulebook: "A vorpal weapon must be a slashing melee weapon." Since a stool is neither a slashing nor a melee weapon, it cannot be given the vorpal quality.
The monk may use this ability to add magical weapon qualities to improvised weapons that could not normally have such a quality, such as adding the disruption quality to a slashing weapon, or the vorpal quality to a bludgeoning weapon.
The real problem with the vorpal stool is that you're spending a metric buttload of ki to give it the vorpal quality, per round. Chances of lucking into a nat 20 in that time? slim.
I've asked James Jacobs regarding Weapon Focus (and similar feats) with respect to improvised weapons. Naturally his response isn't binding, but I do believe he's correct. Essentially it boils down to taking Weapon Focus (bar stool), or Weapon Focus (anker), etc