Yes they do, we have a 1 year old whippet. It's a medium sized dog, and it lives comfortably behind the seats. The whippet only weighs about 16 kg, but has both long legs and "nose to tail".
When we need to take extra luggage it sleeps in the passenger footwell between the passengers legs.
I have built a "dogbox" for the space behind the seats. Its 12mm plywood with some hinges. A layer of foam in the bottom and fleece on the insides makes it comfy for the dog. Covered in IKEA fabric so that the plywood does not rub on the leather interior.
The box folds flat for easy entry/exit from the rear space.
Here are some images of the process, and the finished box:
