Either the 90kN jet or the 120kN rocket alone does have enough power to lift the weight of the car. If you balanced it properly and pointed it upward, firing the jet first and then switching to the rocket when the jet ran out of usable air, it'd definitely go up.
Keeping it stable would be very difficult. The jet and rocket motors are vertically offset; you'd have to reorient them slightly to thrust through the vehicle's center of mass, and the center of mass shifts as it consumes fuel. For use as a supersonic car, its aerodynamics are going to be designed to produce down-force to hold it down on the track; you'd have to redesign it to go the direction it's pointed.
Loren Pechtel's definitely correct that it would have nowhere near enough fuel to make orbit, though.