Generally, no. I'll try to answer this but it Depends on what you mean by "heater core going out".
If the symptom is that you arent getting heat but the fan is running you may have one of several serious problems: low coolant, a broken water pump, or a clogged coolant system. Any of these can lead to an engine overheat, not good.
If you have a puddle on the floor of your car or are smelling a sweet smell when you turn on the heater you could be breathing in toxic fumes. Do not check your coolant level by looking in your radiator with a hot engine; opening the radiator cap with a hot engine can lead to severe burns.
If you are more specific with your question I can possibly give you a better answer.
Yes, as long as you connect the incoming and outgoing heater hoses that were connected to the heater core together. You will not have a functioning heater or defroster but otherwise it will be fine to drive.
you would have to bypass the heater core first.
If water is dripping out of the heater core it is about to go.
To change the heater core on a 1999 Chevy 4-wheel drive, first remove the dashboard and drain the coolant. Unbolt the core from its mounts and remove the dash panel to be able to change the heater core.
Could have a clogged line feeding the heater core. Disconnect return hoses from the heater core and verify coolant is flowing through the core.
heater core hoses not hot
No there is not. Whats the problem no heat ?? If so try this, reverse the heater hoses on the heater core and then go drive the truck and see if you get heat.
Check the heater core, it is probably bad. It could be heater hose connections to the heater core, but I would bet on the heater core going bad.
YES
Simple, take the inlet and outlet hoses going to and from the heater core and connect them together.
NO. Bypass the heater core by connecting the Inlet & Outlet hoses going to the heater core together. Do not plug either hose.
Remove the glove box and you'll have access to the heater core, still not easy.