Heater core/blend door question

Currently the heater core is not hooked up in my Dart. I just have the hose looped back to the intake. I want to hook it up, but my bypass/cutoff valve was rusted out, so I pitched it. Can I hook the core up without the valve, or will heat constantly be getting into my cabin (I.E. the blend door never completely closes)? I know a lot of earlier cars didn't have it, and even today some cars don't have a cutoff valve. Was it only there because my car originally had A/C?