Depends on the situation really.... If it's really hot out and you're pushing the car had yes, the lack of additional airflow could contribute to overheating. I still think it's likely something else contributed or was the primary factor such as the timing being retarded. Check the mechanical and spark timing again.
A "Bosch" relay... youo see them everywhere... they come wir car alarms, foglight kits, Buicks....
I'm surprised your mechanic didn't just wire one in.