Both NII and AF had previously had experience with Aleksei's hemophilia, so before 1912, so I think that they were sure that he would survive. However, there were actual speculations about Heir's possible death:
On October 8th, there was the public annoucement about Heir's crisis which was spread all over the country, despite the real reason of the attack was unknown to the people so they started talk the rumors.
October 9th 1912: The final hour had come. There were only two possible outcomes, and though everyone's prayers were directed towards a miracle it seemed that death was eminent. It was out of the doctors' hands, no specialist could help him. All that was left was to wait.
A priest was summoned to the lodge to administer the Last Rites to the boy, should the need arise. The next day's press release was to announce the death of His Imperial Highness, the Tsarevich Alexei Nicolaievich, Sovereign Heir of the Russian Empire.
Even on the next day, 10th October, Alexei started feeling better. ;-)
