I don't think you have to be a rocket scientist to see that once a horse has already established himself as a great grass horse, that the only thing left you can do to pump up his value is to try and get a good run on the dirt for him so he appeals to more breeders in the US.
Therefore, it wouldn't surprise me if they attempted this.
I have absolutely no knowledge on what they will do, I just see the sense in the Classic attempt.