The exhaust gases must have some rearward component, relative to the ambient air the aircraft is flying through. In that case, an aircraft at mach 2, would indeed have a speed differential compared to it's exhaust gases, of greater than the aircraft's true airspeed. But be careful about speeds here. There's an aircraft at 600 ktas (mach 1?) at -57 deg C, and there's exhaust gases at 600 ktas (mach .8?) at +900 deg C.
Same as a piston/propellor combination. With respect to the air mass the aircraft is flying in, if some air isn't being sent backwards, there's no forward thrust.