I don't know a lot about the internal workings of the Supreme Court - I doubt anyone who doesn't actually work there does - but I don't think Alito would have written up the draft opinion unless there was a reasonable idea of how the vote was going to go.
From what I can understand from people who are lawyers (as I am not), the draft was written to circulate to the other Justices to allow them to see what he had in mind, discuss and debate it, and possibly even change their votes before the whole thing becomes official. For him to be writing it at all, they had to have taken a vote with him in the majority. However, the votes remain fluid until the decision is officially handed down, and the majority opinion can go through multiple drafts.