I have only had to deal with about 6 different dealers over the years, since I stayed working in the same shop, but my experience has been that any of them will take anything on trade......anything to seal the deal and get that new box sold. The dollar amount will vary case by case.
What happens to those trade ins depends on what it is. Bigger / nicer trades are usually sold to another customer on that dealers route and the dealers work that pretty hard - really trying to sell it nearby (my dealer is already priming a few guys to buy my old box now). Sometimes even the cheap / small stuff get bought by another customer who see's it sitting on the dealers truck. Everything else goes home to the dealers "warehouse" and who knows from there.