Other than the obvious advantage that you and your partner can both hunt, is there any mathematical advantage, that is, a better chance of getting drawn going party? Here is what F&G says about how the process works. It sounds like you still only get "one name in the hat" so to speak.
"The computer then randomly assigns a number to each hunt on each valid application. The random number is referred to as your "draw number." Party hunt applications receive one draw number for each hunt. That is, both applicants on the party hunt application receive the same draw number per hunt, so if that number is drawn, both party members receive a permit."