My experience is that the cooling circuit at the back cylinder head, returning to the water pump, needs to be working. Or it can cause hot spots and overtempuratures. Leading to headgasket failure. Then worse. So a blocked heater core is not a good thing, in my opinion.
legend in my own mind
Advice is only as good as the person applying it--
Don't make me give you bad advice!
Lemons or lemonaide, whatever your taste provides.