There's no mechanical reason why it wouldn't, and if you were dead set on having front wheel drive it would be the best option in terms of handling. Just understand that the reason the GTR-LM is FF is for aerodynamics and only because of the way the rules are written. Moving the center of mass forward allows/requires the engineers to increase the front downforce, so if everyone is making roughly the same amount of rear downforce (because of strict rules regarding rear wing and diffuser), a forward weight bias lets you run more total downforce than the rest of the grid, or in the case of Le Mans, the same amount of total downforce more efficiently. Outside of those rules and/or without aero it's just front wheel drive with all of the issues that go with it.
The idea's been around for decades in land speed racing BTW. In fact, the world's fastest modified sports car is a Triumph GT6 that's been converted to front wheel drive.