I am not totally sure that I follow you on this... but here's how I approach something similar.
Just remember that the E natural minor scale and G ( Major ) scale share the same key signature - the same sharp note ( no flats) which is F#.
So for improv in E minor, you can use notes from the G chord shape and G scale, the emphasis on the 3rd of the E minor gives you that minor flavor.
E minor is the relative minor to the G scale. A minor and C share the same relationship.
Back when I started learning guitar I did not hear of CAGED. I learned sort of piecemeal from a book, a neighbor, some basic lessons, more books, other guys who played the guitar, and the Guitar for Practicing Musician magazine. I learned a bunch of chords and a few melodies and simple lead lines at first. I learned the location of notes and bar chords on the fretboard. Then some scales and a little more lead guitar. Maybe not the most organized way, but whats done is done!
I found this on Wikipedia which gives a little related info.
Hope this is helpful. There are a ton of resources on the net now!