No.
51 GOP votes for Alito.
3 Dem votes for Alito.
That's 54 Votes for confirmation so far.
4 GOP Senators who will all likely vote for Cloture but all may not vote for confirmation.
2 Dem Senators who will vote for Cloture.
A yes vote for Alito doesn't transfer into a yes vote on cloture, imo. Some like Byrd have great reverance for the tradition and the tradition is that one can speak as much as he/she wants..... On the other hand, I think he may have voted for cloture on another nominee in the past but not sure.
jmo