The answer is, "it depends".
When I'm learning a piece, I look at the music so as not to get lost and let the fingers find the frets on their own. Once in a while I have to look down to make sure that the position isn't too far off, but generally speaking I can get by. This is step one, getting the program loaded into memory, so to speak.
When the notes and positions are pretty much memorized, I spend more time watching the fingers to make sure they are as close to the frets as the position allows. This is where I focus on the tone of the piece. Using visual feedback on the fretting hand (in my case RH) allows me to devote more concentration on the playing hand (in my case LH) to get the right tone and volume for each note. By the end of step two, the piece typically sounds pretty good.
Next is to repeat step one, matching the tone exactly to the notation markings, relying on muscle memory and building "active" cognitive memory of the music itself. The idea is to get the notes on the page running in my head while my fingers do the work. At the end of step 3 the piece is well and truly memorized.
Once a week I practice after dark with the lights off, playing the pieces I've memorized. It's a kind of test. What I notice is that I get all the notes but the tone doesn't sound quite right. The visual feedback on precise finger positions seems to be valuable, at least for me.
And - on fret markers - I've got a piece of tape on the back of the neck at the 7th fret. It's a habit from the electric guitar where you've got fret markers (that you can never actually see when playing) and 18 frets before the neck meets the body. That way I don't have to look when making a long jump up the fretboard. But I usually do.