Will they?
Who even knows at this point. In the middle of the filibuster the big story could be "Manafort arrested on treason charges!" and the Democrats could easily just never let him take the seat. Everything is all wacky and confusing right now, the Supreme Court nomination is such a minor story, that Democrats really have all the power and political capital in the world to just not do it.
Democrats are really motivated now after watching the GOP fall apart. Would McConnell want to further get them riled up by destroying the filibuster for the Supreme Court?