Making this promise and breaking would make McConnell himself look bad. There is no reason to believe there won't be a vote.
So far, on judicial confirmation, Mitch has done a very good job.
He's not on their side, but he's made himself look bad:
Senate Majority Leader Mitch McConnell (R-Ky.) said Friday that he expects the Senate to vote on Brett Kavanaugh's Supreme Court nomination before the court starts its next term."The timetable typically for recent Supreme Court justices, if we stuck to that timetable and I intend to, would give us an opportunity to get this new justice on the court by the first of October," McConnell told reporters in Kentucky on Friday. linky