Yes, not bleeding the system will prevent the heater core from giving you heat. Since you haven't bled the system yet, you mine as well flush your heater core again. Sometimes, it requires about 3 or 4 good attempts. After you flush your core (with super hot water and maybe some CLR or something similar), consider blowing it out (from both ends) with an air compressor. I will say from experience, this step is the most important. You will see a tremendous amount of gunk come out. The water and solution break it up, but to get it out use the high pressured air. Then, finally bleed the system. Most people who bleed the don't do it long enough, so be sure to bleed the coolant at the heater core for several minutes, not just until coolant comes out the firm time.
I'm changing my heater core right now (as I write). I flushed my core several times last year - and it did work. But, now I'm smelling coolant in the cabin and also the windows are fogging up - which are both signs of a bad core.
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