For eg, if we are learning the key of C, do we need to Learn all triads ie. ceg, dfa etc or can we just learn 7th chord qualities like CEGB, DFAC etc. and those will indirectly give access to the triad enclosed in it? In other words, is there any practical benefit to learning triads, their arpeggios and inversions as opposed to sevenths and is it worth the extra time involved?
Looks like you're constructing triads based on the degrees of a major scale, e.g. 1+3+5, 2+4+6, 3+5+7 etc. This is pretty straightforward in C major as all the notes are white notes on the piano. But it's far less straightforward in other keys. I've just been mentally trying to do the same thing for those triads in C# major - I found this tricky. Constructing and getting familiar with triads like this is complicated enough without having to construct seventh chords for any particular major scale.
So my suggestion would be to start with the triads, and then only add the seventh constructions when you've really got them under your fingers.
The triads are a very good place to start. They're pretty straightforward, and are great building blocks for the next stage.
Which actually is a lot more complex than you think.
The maj., min., and dominant sevenths are only part of the story. Yes, obviously, in a major key situation, there will be (in C) Cmaj7, Dm7, Em7, Fmaj7, G7, Am7, Bo7. But there are also m7b5, aug7 and mM7 to consider. And knowing the basic triad which will need tweaking slightly will help a lot.
No idea whether you're just arpeggiating on a one-note-at-a-time instrument (trumpet, sax, flute), or on guitar or piano. On the formers, it won't make a lot of difference, triads as opposed to 7ths, as you just add or subtract one note. However on guitar and piano, voicings will sometimes considerably change how you play, especially guitar.
I suppose it's like learning any language. 7th chords have their own quality -- V7 is easy to recognize without too much mental wrangling -- but for the others, it can be really helpful to be able to discern the triad first and the top interval next. Especially in, for example, harmonic minor, you've got a different kind of 7th for every chord in the scale! minor-major 7th, half diminished, Augmented 7th (#5), minor 7th, Dominant 7th, Major 7th, and diminished 7th. Until the color of these chords are completely intuitive, picking out the triad first is really helpful. Found a great site for working on this: http://www.teoria.com/en/exercises/c4e.php As for "practical benefit," I guess it depends on what you're doing, but in general more understanding and fluency is better!