Depends. Around here, there is a distinction between a junkyard and an auto recycler. Junk yards remove fluids and crush cars. They don’t care much about the content. Some will dissect the car, separating various materials but they are not interested in component resale, just scrap value.
The auto recyclers will most definitely adjust their offer based on content. This is how they make their money. If you pull the OEM radio, that is something they can no longer remove and sell. You can easily strip much of the value they have in the car and their offer will reflect that. If you settle on an amount and the guy shows up to haul it off, notices you took most of the valuable stuff off of it, they will renegotiate on the spot or worst case, decline to buy it.