It will be painful at first if you don't naturally have good ears, it was painful for me (which is why I avoided doing so on saxophone), but the payoff is huge. It changes you as a musician. I've heard songs on the radio where I knew the chord progression and thus knew how to play the song before even picking up the guitar, that is pretty cool. I might come up with a bit of a song in the shower or in the car and when I sit down at the guitar and figure it out. Neither of these would be possible if I hadn't put in the hours listening to bits of songs again and again.
At the same time, if you are a beginner or intermediate player, I'd recommend justinguitar.com to get started. His youtube channel is extensive, and he and Marty Schwartz were my two main guitar teachers.
Also, I've met people who have played guitar for some time but cannot play bar chords. This simply shouldn't happen. There will be a song you want to play where you will need a bar chord, and you will either have to learn how to play bar chords or learn a way to "cheat" on that particular chord. Bar chords are awesome, piano players would kill to have a movable shape that makes transcription trivial (they'd also kill for a capo). They are well worth the initial effort and once you can finally play them you'll realize that they aren't that hard.
However, what I've observed is that most American teachers don't adhere strictly to Suzuki's methods. Within the space of no more than a couple years, most kids are reading, and using repertoire from outside of the "official" Suzuki books. In other words they're sight-reading by age 10.
Both of my kids now read quite well, but they also pick things up by ear easily, for instance fiddle tunes or even popular music.
Now, I follow web forums for bassists, and the issue of reading is phenomenally divisive. As I understand it, most guitarists and electric bassists learn to play without reading standard music notation, and there is relatively little written literature available for popular music genres. A fair number of transcribed bass parts from recordings circulate in tabulature format.
There is somewhat of a division in the music world depending on reading skill, but plenty of enjoyment to be had on either side. I happen to be both a fluent sight-reader and good ear player, but I'm lucky to play in situations that exercise both of those skills regularly.
If what you want out of music is to press the correct keys in the correct order then reading music will get you a long way. But if you are leaning more towards jazz or pop and making your own music then reading can be a horrible crutch. And the better you are at reading music the more you will rely on it and you rob yourself of developing a functional ear.
And what happens when you fall in love with an obscure indie artist where no transcriptions exist?
Concerning which string on a guitar is used, you can often tell by the tone of the note. Even with muted strings that give a percussive "pluck" you can often tell which note was fretted. For the most part if you are familiar with the style of music you can make very good guesses as to where on the guitar something was played, and if you cannot tell the difference then I would argue that it doesn't really matter.
Finally, out of the long list of musicians I admire in jazz, blues, and pop, I cannot think of one example where they admit they cannot play by ear. In the subset that teach I cannot think of one example where they do not strongly suggest learning music by ear.