Darth Venal said:

Well it is kind of important considering that vote is the reason behind the entire opening of the movie. But anyway, what about The Phantom Menace, how are you getting the Jedi from the forest to Theed? Just having them hitch all the way on the transport and cutting the entire sequence with Jar Jar and the Gungans? I'm asking out of interest, not challenging you.

Confusedmatthew and his video reviews of the first 2 prequels explains it best how the voting system in the senate is ridiculous and makes no sense. Amidala and her ONE VOTE gets a Supreme Chancellor re-elected, and similarly, Jar Jar, and his ONE VOTE gets the Chancellor granted emergency powers to create a clone army that the entire senate were dead against having. They passed a motion to circumvent themselves!

So no. Jar Jar's one vote isn't important at all. It just shows how Lucas wasn't even thinking when he made this film. When he needs things to happen in the plot, everyone suddenly becomes stupid to allow it to happen.