There are roof racks available which cover only one falcon door. Alternatively you could just put the kayak inside the car.
Now that I think about it, I haven't even seen the back open. Why can't I find pictures from the back, with the gate open?
In the presentation the middle row seats inclined forward. On the Model X webpage it says the back row seats fold flat. You could definitely fit a whitewater kayak in; a downriver kayak would be tougher. Perhaps you need the configuration with two seats in the second row (instead of three) -- that should be enough room to fit a kayak between. That said, I imagine the second row seats will fold down.
But you could just put it on the roof :)