I will assume you are referring to a Controlled youth hunt. A youth that is between 12-17 at the time of application can apply for a Youth Controlled Hunt. If they are successfully drawn for the hunt and they turn 18 later in the fall they can still participate.
If the hunt is a general youth hunt (Not a controlled Hunt), the age requirement still applies. For example, there is an early two day youth waterfowl hunt for hunters 10-15. In 2012 this occurs Sept 29-30. This is not a controlled hunt. So, if the hunter is turns 16 prior the 29th they will not be able to participate as a youth hunter. If their birthday is on Sept 30, they could hunt on the 29th, but not on the 30th. Of course they can hunt during the general waterfowl season beginning at age 10.