The area around the State park is a bit tricky. Yes you can hunt it and yes there are antelope around but it seems that they move off over to private with pressure. Also the restrictions can also limit where you can get to without the use of a boat. Most of the good spots that hold animals are away from the roads and are landlocked. More info here
Wyoming State Parks, Historic Sites, & Trails - Hunting - KEYHOLE
The antelope population is just coming back in that area so numbers aren't bad. If you start now, you might get your foot in the door to gain access to some area ranches that might also border other state lands thus increasing your acreage that have antelope. For what it is worth, I would suggest a different area that has a few more tags available and thus more antelope. With the limited number already, you can bet the tags will go quickly. There is quite a bit to do in the area so not a bad first western hunt. if you want to shoot me a PM i'd be happy to help you further.