No, it is not an allowed charitable deduction. You get to deduct what you paid over/above market value.
They have bought something at market value, not in excess of market value. The market value is established by the bidders they are competing against who are willing to pay the same price, or close to, for the same special opportunity.
They are not bidding on a $1,200 elk tag from UTDWR. They are bidding on the guarantee. They are bidding on moving to the front of a very long line, with a correlation that the longer the line the more they are willing to bid. They are often bidding on not being confined to the season dates or geographic confines of drawing a tag for Unit X. They are bidding on an opportunity that lets them keep their place in the preference/bonus point line. The list goes on and on as to what they are paying for in excess of the draw tag any of us might acquire. They are not making these same level of contributions absent a special hunting opportunity, establishing even more so that the value of the special tag represents what they are paying for it.
Some say they tax this purchase can be claimed as a charitable deduction. Taking the deduction on your taxes and defending it under audit are two different things.