I believe it to be very important to understand what you’re playing. If you don’t, you just read notes off a page and reproduce them so your performance is flat and unemotional. No notation can describe an emotion. Loud or soft is certainly not an emotion, just a volume level – and there’s no musical notation for “this bit is supposed to make people laugh” or “make them cry here”.
Going further, even J S Bach wrote chord sequences. If you just slavishly follow the notes but don’t understand the chords (harmony) and why it moves as it does, it is much harder to learn. There’s logic in the harmony (especially in J S Bach!) and if you know the logic some of the learning is automatic.
So it doesn’t matter whether you’re learning something by Mozart or by Kings of Leon, you’ll do better with some understanding of why the notes are written as they are.