I should think that this would depend upon the precise nature of the device employed. The usual method involves broadcasting signals on cellular telephone frequencies: by using jamming signals that are stronger at the target telephone aerial than those from the nearest cell repeater, communication is interfered with. Jammers are available with various power output levels. A low-power jammer, with a level comparable to that of a cellular telephone (which would be sufficient to stop communication within a smart car cabin), should not affect the circuitry of the car, since we know that the latter can tolerate cellular telephone use. A higher power jammer might cause trouble, though the frequencies involved are much higher than the spectrum region most likely to cause trouble to the car.
However, a different jamming scheme, such as a high-power, broad-band jammer, which can jam a wide range of radio devices, would likely cause trouble to the car circuitry. Most cellular telephone jammers are not of this kind, as far as I am aware.