Of course they would.
In fact... the reason any of this is possible is because they tried to rig the system in their favor under Obama. They couldn't get what they wanted, so they changed the way the game is played.
The old rules of the senate stated that 60% of senate must vote to confirm a nomination. The democrats did not have 60% of the votes the last time they nominated someone to the bench. The Republicans refused to compromise, and so the Democrats changed the rules of the senate so that only a majority was needed to confirm a nomination. Only 51% was now needed... and the Democrats confirmed their appointee over the Republicans objection.
Mitch McConnell warned them back then that this move would come back to bite them in the ass... and it has.
Donald Trump has already nominated 2 judges to the bench of his choosing. Now he gets to nominate a 3rd, and there isn't anything the Democrats can do about it except cry and gnash their teeth. This wouldn't be possible without negotiating with the Democrats under the old rules, because Trump doesn't have 60% of the vote... and that's why the Democrats are all bent out of shape and making wild threats... because they shot themselves in the foot.