Yes but without the D so it would be 20x212, and that’s why it’s not a D7. If you were to add another note it would be D#, so 201212, pretty awkward for the fingers.
But your observation brings up a natural sounding way to use a dim chord. You can turn a D7 into a D#dim just by walking the root note up half a step, then you can walk the root up another half step to E and play an Eminor. I think Pink Floyd do that somewhere in Dark Side of the Moon.
Yeah, it’s the top three notes of a V7 chord, so it wants to strongly resolve to a I (in the OP’s case, the F# wants to move to G and the C to B, the same movement as in the V7 chord, D7).
I personally don’t see vii chords much at all in popular music.
One way of thinking about the 7th chord is that it has a tritone interval between the 3rd and the 7th notes. In G major the V7 chord is D7 (DF#AC), thus the F# to C is a tritone (diminished 5th). That’s why neither the Dm7 (FC), or the Dmaj7 (F#C#) have as much need-to-resolve as the D7.
I believe the traditional analysis would be that it’s borrowed from the parallel minor. You can also say that it’s a IV of IV, especially if the progression goes bVII, IV, I. (In other words, in C, the progression Bb-F-C, Bb to F is a IV-I movement if F is the tonic. Since F is the IV of C, the Bb can be thought of as the IV of IV.) You can also look at it as modal interchange with the bVII being borrowed from the mixolydian.
Traditional theory is not always very clean trying to analyze popular music. When it returns immediately to the I, I kind of just think of it as as a very soft cadence. So like if V7-I is a strong, “perfect cadence” and IV-I is a weaker “plagal cadence”, bVII-I is a softer version of that to me.
When the bVII is followed by IV, then it just feels like a IV-I to me centered on the IV chord.
Good analysis. That exact move appears in Davey Graham’s “Lashtal’s Room,” and it sounds as described. The fourth of the fourth before returning to the tonic, without much fuss or harmonic tension.
Posting again to avoid messing up the imbedded video with an edit:
I’ve just checked on the guitar to be sure, and it actually happens twice in that part of the tune. Just before the part I indicated, it’s in G, with the cadence F-C-G. The part I indicated is in C, with the cadence Bb-F-C.