you can if you want to take a chance of something happening to the string while it is in the back of the truck, even in the back seat of my truck I have stuff sliding around and anything could catch the string and with all the tension on it, it would be a lot easer to cut and that is a lot of energy stored in the limbs.
You can put your target in the back of your truck and carry it with you hunting. then use the truck headlights to light up the target.
Just remember it is your bow you can do with it as you wish.