I don't see how it was to any disadvantage, since the whole point was that he was in denial of the War Doctor's existence. He was "the man who forgets"...and does it deliberately.
Does he though? Everything we saw the War Doctor do are things the Doctor openly talked about doing anyway, the Time War, the supposed mutual genocide of the Daleks and the Time Lords, the Fall of Arcadia. He continues to talk about everything the War Doctor did while supposedly denying the existence of the War Doctor.
In a way it makes sense that this was the first incarnation to make any show of his number as part of his identity, since it helped facilitate that dissociation.
Thing is, none of that was the intent. How could it? Moffat didn't even create the War Doctor until after he knew he couldn't get Eccleston for Day of the Doctor.
The 11th was on a propaganda campaign. The Doctor lies.
That doesn't work for everything. The hotel room being room 11 in The God Complex is meant to be the hotel revealing a hidden truth about the Doctor, yet it allows him to maintain the lie of his numerical designation? Then again, the confession dial was also about the Doctor's hidden truths and still identifies Capaldi as the Twelfth, so who knows.