Diesels are seriously heavy motors, especially a V8 version, when compared to a gasoline engine. It would make the car very front-heavy, so a straight-line or burnout/exhibition car would be probably be as far as it would go. It probably could be done, if you got a wrecked 3/4 ton diesel puickup truck as a parts vehicle for example (not cheap, even in wrecked form). You'd have to probably make a custom k-member and possibly modify the tranny tunnel/firewall to clear everything. And put a huge rad. in it. As well as a built rearend to handle the torque.
I've seen one project where a guy stuffed a Triton V10 (gasoline) truck engine into a Fox mustang, so it goes to show that with enough fabrication you can stuff some serious cubes into these cars.