That RX7; Although it has 'Falken' in it's name, it doesn't have the livery, so I guess that the answer to your question just like it has been said above. No, the Falken GT-R R34 is the only car with a Falken Livery.
It has nothing really on the car to even suggest that it's associated with Falken apart from maybe the tires? Which in this game it doesn't show/matter/affect on the car.