As Gene indicated the points would usually be the first to fail. Coils generally draw about 3.5amps so it will never trip the breaker unless there was a short to ground.

I don't think a coil could ever trip a 30 amp circuit breaker. Also, I was under the impression that if the ignition was left on with the points closed the result was burned points rather than the coil failing. Just my opinion and experience. 

I have an aftermarket 30 amp circuit breaker on my main electrical feed from the battery. If I forgot and left the ignition on (before starting) and the distributor/points were in a bad position, would the coil likely overheat/fail before the breaker tripped (assuming my grasp of electrical basics is accurate)? The breaker automatically resets when it cools, so any coil overheating would be repetitive.

6 VOLTS/POS. GRD. NW INDIANA