No, I don't think Scars
has changed anything in that regard. We never knew if the Khagan died or not, only that he was lost in a similar fashion to several other Primarchs. I believe Scars
was just precipitating this.
If Horus had handled the situation with more care, it seems quite possible that he either could have gained the allegiance of the White Scars or perhaps removed them from the conflict altogether.
The last few novels in the series have certainly given us a taste of the disunity of the rebel leadership. We know that the vast majority, if not all, of the traitor Primarchs had alternate agendas and were not steadfastly loyal to Horus. Mortarion's admission (pre-acceptance of Nurgle) in Scars
was very interesting.