If it were a TV or a radio then using a car battery and coil of wire would certainly produce interference - if you had (say) a thousand turns with a total resistance of say 1.2 ohms (probably using litz wire), you could generate a magneto motive force (MMF) of 10,000 ampere-turns each time you connected or disconnected from the battery.
How would this directly affect electronics that might be several cm inside a box? Say the most sensitive electronics were 5cm inside and say the coil were a couple of cm deep. The best round trip I can imagine for magnetic fields to make would be about 14cm but this will almost certainly render the effect nearly useless.
An air-cored coil projects flux all the way around its coils and maybe 1% of the flux would penetrate at this depth. This would lower your effective MMF to about 100 ampere-turns and, the length of the field (14cm) that this 1% can reach, implies a magnetic field strength (H) of 100/0.14 ampere-turns per metre = 714 At/m.
This level is about what you would see on a ferrite cored switch mode power supply and this doesn't appear to cause very local chips or components any trouble.
What if you used a ferrite core to "focus" the magnetism in order to damge an electronic component. This doesn't work - there is still the totally dominating air-gap from one end of the ferrite to the other which the magnetism has to flow - this air gap is the dominant factor - now matter how much ferrite you have - even a 1mm air gap can reduce the effective permeability of a ferrite core by over 50% on most reasonably sized ferrites. So what if your coil only had a 1mm air gap - it would be totally useless at being able to damage components more than a few mm from the air-gap - the field lines would fringe around the air gap but would naturally take the shortest path back through the ferrite - leakage flux would not be much.
If you wanted to improve the mechanism you could use a powerful (but simple) power oscillator and tune your coil with a capacitor to make it resonate. I've seen this done in pharmaceutical metal detectors tesing all manner of drugs for metal content BUT, does this affect the product being tested as it falls through the mouth of the detector and directly thru the plane of the transmit coil? No it doesn't - even foodstuffs like chicken and beaf are passed through resonant-coil metal detectors and there is no heating effect or bubbling even though probably 50% of the magnetic field actually passes through the salt-water saturated meat.
Try looking up equipement called "eddy-current heaters" to satisfy yourself on this.