No, it will not.
An ability that triggers when a permanent “becomes untapped” only triggers if something goes from being a permanent on the battlefield with the “tapped” status to being a permanent on the battlefield with the “untapped” status. (Things that trigger when something “becomes tapped” work similarly, just in the opposite direction.)
Undiscovered Paradise starts off as a permanent on the battlefield with the “tapped” status, but goes directly from there to being in your hand. It never exists as a permanent on the battlefield with the “untapped” status, which means it cannot trigger
Mesmeric Orb.