This is a poor solution for the reasons ZENITE has explained: you don't want a pick/ban champion being taken by the enemy team because your last pick wanted to play it (even if it would realistically be taken before their turn was reached).
While there is nothing wrong with Shaco jungling, I personally prefer not to have one on my team. Most of the Shaco players I have seen are not very good with him, Shaco falls off quite badly in teamfights (regulating him to split-pushing or picks), and he offers very little utility to his team.
In addition, Shaco's lack of CC and durability from a position which typically provides one or both can really screw up team compositions. For that reason alone, I dislike seeing him jungle while on my team.