Isn't it interesting tht both Woody and myself answered xzin's question in the affirmative, but you state that Calvinists must answer it in the negative. So much for granting your opponents the charity of understanding their position.
What you don't realize is the fact that God's election is a complete package, i.e. it consists of His gracious choice and the application of His grace to the sinner all the way to glorification. You assume that we must believe that it is limited to His choice, and does not consist of the entirety of His redemptive work.
My point is that if "Y" is not "chosen" then no matter how much God reveals himself to that person, he will not respond to the Gospel message. Am I wrong?