The advantage of the heptatonic system is: 1) it adds 2 fingerings that are often left out in the conventional CAGED system, thus covering every fingering possibility available for any 7 note scale throughout the guitar’s fretboard. 2) It organizes the scales for easier visualization and relational categorization into practical cycles when playing horizontally or vertically on the fretboard.
Yes, I do recommend relating to the scales/ arpeggios that they generate. Keep in mind though, that there are many voicings generated from each of the 7 fingerings for each chord type. This is a subject to which we would have to devote a whole course and which I plan to do so in the future. However for now, I briefly touch on the subject in the Chord Studies that are available for voicings on strings 1,2 3, & 4. Furthermore, when looking at the PDF for each fingering pattern from the Scale & Arpeggio Fingerings book, in addition to the tab and notation, there is a fretboard diagram that shows the arpeggio in white circles. You can easily deduce what voicings or shapes are related to the pattern in question.
Here are the initial 3 fingerings that I introduce In relation to the CAGED system :
Pattern 1 generates an open E shape
Pattern 4 generates an open A shape
Pattern 5 generates an open B shape (although this is not part of the conventional CAGED)
Hope this is helpful….