You should be able to get a check for the truck and keep the truck. My daughter's car was totalled, but driveable, a few years ago. Got a decent check, and kept driving the car for several years. If you don't get a settlement that allows you to keep the truck, you likely won't be able to sell anything that was on the truck at the time of the accident, or at least was on it when the adjuster saw it. On the other hand, they often don't consider anything other than the basic vehicle when they offer a settlement.
Whether you can remove anything also depends somewhat on where the truck is now. If it's at the towing company's lot, you won't be able to remove any parts without the insurance company's ok. I was allowed to pull the 3 good tires and wheels off my son's wrecked Mountaineer as part of the settlement as long as I put any sort of tires and wheels back on it, and it was already at the auction yard. Check with the insurance company before removing anything visible.
Another thing you might use to your advantage if you want to try to keep the truck and part it out - the insurance company might have to pay significant storage fees on your wrecked truck if they keep it. My totalled Bronco II was stored inside for 6 weeks or so after the wreck, and the adjuster told me they had $700 in storage fees, about half of what they paid me for the Bronco II. They might have gotten $200 from the salvage yard for it.
