Is it really possible to know which chords go with which notes in a song without having to depend on the written sheet music? Can you pick out a song by ear and then harmonize that tune with chords that match it?

It is quite possible to predict which chords will occur in a given song, once you know the key and understand the "guts" of music theory & chord progressions.

What I'd like to discuss today, is whether or not is it, a) viable, and b) better, to learn how to play the guitar by methods of learning online.

If you want to do anything in life, the best way to do it is to find someone who has already done it before you, then model off of them.

There are a number of locations where free, basic guitar lessons can be found.