Mookie;
If I saw signs of visible leakage, or the coolant level was dropping (and I could attribute the drop in coolant level to the heater core,and not some other leak like the water pump etc.) then yes I would replace it. But I have been driveing it for several thousand miles like this and my coolant level has never dropped more than one cupfull over a years time and 6,000 miles, and it can lose that much just to evaporation from the resevoir tank. Heater cores usually don’t suffer catastrophic failure, they just seem to seep.
Before you replace it you need to BE SURE this is what it is, AND I AM NOT SURE. I AM JUST GUESSING. Labor is going to be expensive, especially if you have a.c., so I would wait untill you can actually see coolant leaking out from the bottom of the heater box, or where ever the lowest point would be. Your heater box may have a drain to the outside of the car so you might check there too. Put some newspapers under your car at night and check them in the morning. You may find you have a few oil leaks too.
One more thing to consider, your fresh air/ventilation system picks up air from the outside of the car. This smell could be comeing in from the outside (from the engine) and getting recirculated through the f.a.system. Like the others said it could be an oil leak that is burning on the engine, riseing up around the hood gaps and before it can be blown away it gets sucked in the f.a. system. Next time your engine is warmed up to operating temp. pop the hood and stick your head under there and see if you can smell this same smell under there. Keep us posted.