A "Special Edition" of Doctor Who Magazine titled "The Year of the Doctor: The Official Guide to Doctor Who's 50th Anniversary", reveals that early incomplete drafts of the anniversary special by Steven Moffat did feature the Ninth Doctor rather than the War Doctor, though this had been changed to the War Doctor by the time Moffat wrote a complete draft of the whole story. From p. 13:
Steven's take was that what the Doctor remembered about the Time War might not actually have been what happened. Steven's idea fitted a narrative featuring the three most recent incarnations of the Doctor; the Ninth played by Christopher Eccleston who may have been involved in the war (despite a suggestion of being newly regenerated in 2005's Rose), the Tenth played by David Tennant, who was still concerned by the conflict, and the Eleventh Doctor, who had learned to be more at peace with his actions. Steven knew David as a friend and as a devotee of the show to be sure that he would do everything possible to be available for the project, but was concerned about the availability of Christopher Eccleston, who had left the series after a single year in 2005.
And also on p. 13, there is a sidebar titled The Time War: Draft Scripts which begins:
Prior to full draft scripts of Doctor Who: 50th Anniversary Special there were incomplete drafts headed Doctor Who 50th Special: The Time War. A 'Partial Draft' dated Monday 14 January 2013 was fundamentally the same as the start of the finished programme with minor changes. Osgood was Kate's 'harried PA' and did not have a scarf, and Kate had the helicopter rescue the TARDIS because whe believed it was being attacked by a motorcyclist. The main differences were that the figure in the ruined building on Arcadia was the Ninth Doctor and the Moment was 'a girl in rags... young, elfin-faced, beautiful. A mass of hair and a feral stare' (referred to in stage directions as 'Raggedy Girl'). The Raggedy Girl explained that the barn was a crucible in which she would test the Ninth Doctor's worthiness. When the girl showed him his future, the Ninth Doctor was sucked through the portal she summoned up and dropped into the forest clearing next to a cottage to meet the Tenth Doctor and two Queens. The Tenth Doctor's encounter with the Zygon was then narrated through to the second appearance of the portal in 1562 through which came a fez... and the script ended.
P. 18 of the magazine talks about how the Ninth Doctor was replaced by the War Doctor:
By mid-February [of 2013], Steven had a third partial draft of The Time War but resisted writing a full script, since he was concerned about Christopher Eccleston's availability, and he also had doubts that it was the Ninth Doctor who had fought in the Time War. Steven had a couple of enjoyable meetings with Christopher to discuss his involvement and the direction of the story. In The Guardian, Steven explained that the pair had enjoyed a "very amiable and gentlemanly" conversation and that the actor considered the project "quite seriously" before turning it down. "It's just not the sort of thing he does," explained Steven. "But Chris was perfectly sweet and kind about it." Speaking to DWM Steven admitted, "I sort of knew, despite a valiant attempt, that I wasn't going to get Chris Eccleston. He was lovely about it, but it just wasn't for him."
Rather than being a major blow, the actor's non-involvement opened up the story for some even bigger surprises. Steven toyed briefly with having the Ninth Doctor's role carried by the Eighth Doctor, but could not reconcile the warrior Doctor with the incarnation played by Paul McGann in the 1996 TV Movie. Then the writer recalled watching The Five Doctors in 1983; for this story, the First Doctor had been played by Richard Hurndall, cast since William Hartnell — the original First Doctor — had died in 1975. While Hurndall's performance was effective, Steven had been aware that it bore little resemblance to Hartnell's Doctor... almost as if this was an entirely different incarnation who had also engaged upon other, untelevised adventures. This notion of a 'mayfly' Doctor who appeared for just one show was something Steven had previously considered, particularly if a major movie star could be persuaded to guest as a future incarnation. The opportunity now arose to introduce an incarnation of the Doctor who had fought in the war and who had never been talked about. This incarnation wouldn't even refer to himself as 'the Doctor' because of the terrible decisions he had made during the Time War. This new incarnation could offer the age and the irritability of the First Doctor as in The Three Doctors; a Time Lord who had existed during the nine years between 1996 and 2005, whose adventures had never appeared on television. "What was he up to?" pondered Steven at the ExCeL. "What was he up to when we weren't looking at him...?" Such a part would be able to attract a major star.
This page even shows some bits of a storyboard with Eccleston's Doctor:
Another recent article in which Moffat talks about the chaos behind the scenes in the planning of the anniversary special can be found here. Moffat seems to say that the decision to have a "hidden" incarnation, and the hiring of John Hurt, were both last-minute matters, with Moffat indicating that after finishing the script he only had about two weeks to find an actor:
He was top of our list. I wrote the War Doctor script and we sent it off to John Hurt, assuming that was the beginning of a frantic two weeks of sending it off to every actor you’ve ever heard off and got Janette Krankie. And – God bless him for ever! – he said yes almost immediately. That was the first stroke of luck we had on that sodding show.
As a side note, Mike Edenfield's answer says "everything we know about the history of the Ninth Doctor tells us that he had just regenerated when he shows up in Rose, to the point where he's still looking at his new face in the mirror", but in fact another recent issue of Doctor Who Magazine shows that this was not the original intent of writer/showrunner Russell T. Davies. From the May 2015 issue (Issue 485), p. 42:
The Doctor saying "Look at the ears" as he looks in the mirror was added in the second draft, and could be taken to imply he has only recently regenerated. DWM asked Russell if this was meant to be the case. "Well, I hate being prescriptive here, cos sometimes, when I give an opinion on a scene, because I'm the writer and producer, it can become a fact. When I much prefer it if you make your own mind up. But enough time has passed now so, for the record... No, I do not think he'd just regenerated. If you have certain physical features like big ears, or buck teeth, you look at them and sigh at them every time you look in the mirror. And I think, if you'd had eight different faces, even if you'd been in this current form for a hundred years, you'd still mutter at them. So it was meant as a nod to the fact that he'd once had other faces. But I wrote the Titanic stuff and Krakatoa assuming that the Ninth Doctor had been around for a while. He doesn't act very post-regeneration, does he? He appears in command, waving a bomb. This is a man who knows himself, and has known himself for a while."
(The "Titanic stuff and Krakatoa" refers to the scene later in the premiere episode where Rose meets up with an obsessed Doctor-tracker who has found some old pictures of Chris Eccleston's Doctor reappearing at various points throughout history, including the Titanic, Krakatoa, and the JFK assassination)