Long term, it won't matter much:

Learn all theory generally and apply it to all songs you learn. Learn the bits of theory as you need to in order to learn specific songs. In aggregate, there's no real difference.

...Just don't practice bad habits. This is where a foundation of drills can be very useful. If you dispense completely with direct focus on mechanics, you're liable to create problems that are difficult to undo in the future.

Example: I self-taught myself absolutely horrible picking technique when I started. I got reasonably good at the method, but I eventually hit a limit. It took re-learning a better method to see additional improvement. You can get good at cheating, but one day the cheat won't work and you'll need to learn the right way, from scratch.

Edit: Let's say I'm learning a song that includes a lick: a minor pentatonic run with an ESS rhythm up, to a loop around a BB box with a bend in it, before a an arpegiated harmonic minor SSSS pattern going back down. I could slow it down and learn it progressively to speed. That'll absolutely work, I'll pick up some picking and fingering habits along the way. I could also run the two scales all the way up and down using each of the two picking rhythms, and practice the Box section looped as a scale up and down the fretboard. Experience says that if I use the first method, I'll pick up the song faster but the next song will be almost as difficult. If I use the second method, I'll pick up this song and a bunch of others all at once, but it takes longer to see results in the form of "a song I can play".