Or would I have time to bring the animal back to my truck and drive it all the way home before any processing is started? (Likely 1.5-2 hours after the initial shot)
Yes. Bleed and field dress the hog and head home.
It is important to field dress the hog ASAP. Do not burst the bladder and contaminate the meat. Be careful not to cut the intestines or stomach.
Much of my hog hunting is done in hot weather and I've got it down pretty good. When the temperature is 80 degrees one has about four hours to get the meat cooled before it begins to go bad. My truck has a large cooler with three or four frozen one gallon water jugs. Last week I killed a big sow with the temperature at 95 degrees F.
1. Hung the sow from my pickup game hanger.
2. Cut the animals throat and let it bleed out. This improves meat quality.
3. Skinned the hog.
4. Field dressed the hog.
5. Placed the carcass in the cooler.
Elapsed time from shot to cooler about one hour, 20 minutes. A big pair of limb loppers are great to cut off the legs and head. Skinning pliers also save time.
Good luck with your hog hunting experience.