NO, as long as you bypass the heater core on the engine side of the firewall you will not have any problems.If I dont replace the heater core and hose right away will it do damage to the car?
I never had an issue getting enough heat due to the full exhaust. Lots of heat through the firewall and floor. When my heater core went, I had alot of issues with my defrost fogging the car up worse than it cleared it. And the air smelled a little funny with the antifreeze being piped into the vents.