Not really. Here's the problem:
1) the pipes from the heater core protrude two inches FORWARDS through a very small hole in the firewall
2) the heater core is very firmly wedged in the climate control box, and can only be removed SIDEWAYS
Attempting to pull the pipes back can't be done, because the heater core won't move back in the climate control box
Attempting to pull the heater core out of the climate control box can't be done because the pipes won't move sideways in the firewall
In my first picture you can clearly see the complete climate control unit (dead centre beyond the gearstick). You must remove this too, in order to replace the heater core properly.
You CAN remove the OLD heater core without getting everything out, but you WILL break it.
You can NOT install a new heater core without breaking it also
In fairness though, once the dashboard is out, it's REALLY easy. Five screws and you can tug the whole climate control unit back from the firewall, and do your thing.