Yes you can never tell for sure, but I think a goal from Mbappe would have shifted the momentum at least a bit or it would have changed the game because Real Madrid wouldn't have to open up anymore and play for the win. They I think would have been ok with the draw and then they would have been the ones who could patiently wait for one attack and score a goal. But since they were behind, it was impossible for them to stay calm and patiently defend. There have been plenty of games where one goal changed it all. Should I provide an example? Manchester City vs Feyenoord Rotterdam 
In your example, you don't need to go far, just remember Real and their games, especially in the context of the Champions League, for example last year against Manchester City, when they only needed to score one goal for the opponent to fall apart, get confused and start conceding more goals. It could have worked, but I think not with Liverpool.....
Yes yes I know, Real Madrid has made the impossible suddenly possible out of nowhere so many times in the Champions League against the best teams in the world that one goal can change so much for them. But I have to say that the team they have available now is not quite the team they had available when they did these crazy turnarounds. But still at 1-1 you don't want to run into a counter attack with Mbappe waiting for it to be finished. Liverpool would have been more careful, but after he missed the penalty, they could just play their game.