I would say no. I replaced the heater core in my '98 last winter. Even if you could remove the dash pieces, (mine is cracked pretty bad also) there is the air bag pod to deal with. The way the water lines run through the dash would make it very difficult to remove it even if possible. The entire air box has to come out of the truck to remove the core. My dad and I did it in about 9 - 10 hours. We were able to move the dash and hang it from the passenger grip handle rather than remove it completely. I have pics and will post them. They are not the best but I took them with my cell phone.
Just FYI - you have to evacuate the a/c system and then have it recharged.
If you don't the compressor will not come on and you will have no defrost.