When I began piano lessons as a kid, I memorized the pieces instead of learning to read the notes. It did me no favors. Yes, I could play a piece nicely, but if my instructor asked me to stop and start again, I couldn’t do it…because I couldn’t read the music, so I didn’t know “where” in the piece I was supposed to pick up from.
Now, learning the violin, I told my instructor that I wanted to learn to read the notes rather than memorize it. Now, when she stops me, I’m able to resume playing from anywhere she asks. With that, after playing a particular piece enough, I do naturally memorize it but still follow along with the sheet music.
I will say, though, that in the 2 years I’ve been playing violin, I’ve learned to “hear” when my intonation is spot-on, flat or sharp. So, Anteros, in my experience, you learn to play be ear with experience. Just as the others have stated, when you listen to a song that you’re familiar with, you begin to hear when the notes are “off” and how you need to adjust your fingerings.