As resistance goes up, as in the case of dirty contacts, current goes down. As circuit breakers are current sensitive, I don't think that problem would trip a breaker. On the other hand, your light output would suffer and your chances of a fire go up. So, low resistance connection are indeed necessary.
As always, installing a current relay is a good idea. It takes the high current loads off old parts like headlight switches and dimmers. Bad connection problems can be minimized as the operated at around 50ma (0.050 amp).
