Nope - tried.
The photos on the Kuat site show the hatches that open from bottom to top and those that drop like a truck. I don't think there would be any problem with either of those based on my observations, but with the Jeep tailgate that opens like a door, it doesn't. My spare sits higher than stock since it is a bit oversize, but even if the tire cleared, the door would hit the rack.
Like I said, not a deal killer for me since if I need trunk access I can take my wife's SUV or my other car. It's just a first world problem.