This is unknown. We do know that Steven Moffat really wanted Christopher Eccleston to be in the 50th Anniversary story. We also know that when the villain in "Prisoners of Time" (comic story) is speaking of the various Doctors, he refers to the Ninth Doctor as "The Solider". In addition, "The Gallifrey Chronicles" (novel) describes the Doctor who fought in the Last Great Time War, and it is clearly describing the Ninth Doctor.
If Eccleston had agreed to be in "The Day of the Doctor", would there have been the War Doctor played by John Hurt? Only Steven Moffat knows that.
Steven Moffat has revealed in interviews that the War Doctor was created and cast to take the place of what would otherwise have been Eccleston as the 9th Doctor, had he agreed to take part.