You can but you still won't be able to get it out.
how to replace a heater core in a 1997 Chevy blazer
how do i replace a heater core in a 2001 Chevrolet blazer
The separation between the engine compartment, and you, is called the firewall. The Steering shaft, from your steering wheel runs through the firewall, the heater hoses run through the firewall, the power brake vacuum unit is connected to the firewall, your ignition wires etc run through the firewall.
with your hands
Mounted on the inside of the cabin, on the firewall, passsenger side.
take heater hoses off the firewall heater box and unbolt heater box on the firewall and then pull heater box down from under the dash and you will see the heater core inside, replace it in the box and bolt everything back together.
What you have to do, is replace the heater core itself
heater core has a leak replace heater core
The heater core on most GM vehicles is located behind the dashboard. You must remove the entire dashboard to gain access to the heater core which is mounted to the backside of the firewall. try this: http://www.zr2usa.com/mboard/index.php?showtopic=19527&st=0&#entry405342
Inside engine compartment passenger side at firewall
The heater door control on a Blazer can be replaced by purchasing a new one. The heater vent will pop out with a little nudge from a flat tipped screw driver. Then insert the new heater vent door control.
Open both front doors and remove everything between the firewall and the front seat :(