63 Dodge Dart, now let me see;)

No need to fill the radiator anywhere above the cores, that excess will always puke out.
Since the motor is out, that is always a good time to replace the water pump, cheap at Rock. But I always have bad luck with old radiators, water pumps, and distributors!!!!
No, not in this case it will not. She needs to fill it slam to the top because it's going to burp the air out. It's never done that yet, because it's been puking with no thermostat. It might blow a "little" out the overflow, but at this point I'd want it FULL so she will not have to remove the cap with it hot to fill the radiator after it warms up.