In a perfect world yes. But many of today's cars DO NOT have a heater
control valve, they use a "blend door" to control the amount of heat in the
car. Weather this car does or doesn't  have one doesn't matter.
Whenever the system gets air in it as with a radiator replacement, the
heater core gets full of air.
The expansion tank ONLY works to its full ability when the car gets to full
hot, then back to full cold. It is useless for eliminating massive air from
a system, in fact you can have the car overheat with a full expansion tank
and a air pocket. the cart will overheat AND be reading cold on the dash.
In my learning years in this field, I sent a car out of the shop with air in
the system. It overheated. The primary symptom was a cold heater.
This method is merely a easy, quick way of getting most all of the air out
of a system that has been worked on. The lack of heat is a symptom of
something else; and re-reading the original post I would be convinced he has
air. Now he still needs to replace the rad to prevent other issues in the
future.
What good will getting the air out of it anyway do when the waters going to
leak out again.