Disregarding the sevenths for simplicity, if you go from
VII - meaning the tonic major chord to a major chord rooted on the leading tone - and you want to see functional harmony, an example that comes to mind is Red Roses for a Blue Lady. In that song the chords are
C B7 E7 A7 Dm7 G7..., which is clear a series of secondary dominants.
Obviously the secondary dominant chords are different that your
VIImaj7 major seventh chord, but the difference is in the quality of the sevenths, not the roots. The initial root progression
I VII and the triad portions of the chords at least suggest, to me, the sound of the opening to Red Roses for a Blue Lady. It adds a sort of sophisticated sound to a basic blues progression, depending how you play it, I'm thinking more jazz than something like barrelhouse blues.
In regard to functional harmony you should consider what chord comes after the
VIImaj7, what comes next has much more importance for function that what chord came before. If you just go back to the tonic, like
I VIImaj7 I, you don't have much for functional harmony, and the movement is more of an auxiliary movement, a neighbor chord.
...or should I say #VIImaj7 if we are assuming blues so possibly mixolydian modality
Just a technical note, Roman numerals are relative to either a major scale or a major/minor key, depending on which convention you follow. Roman numerals for chords rooted on the seventh scale degree are particularly confusing and inconsistent compared to other chords. But in jazz I think I've only seen Roman numerals in relation to major scale degrees. So, the common ones are
viio for the diminished leading tone chord, and
♭VII for the minor subtonic chord, or as you pointed out, it could be the mixolydian subtonic chord.
VII is less common, but should read as "major triad root on the leading tone."
♯VII is confusing, because it looks like "major triad" rooted on a leading tone raised a half step, which would be enharmonically equal to the tonic. I think you should label
F7 Emaj7 as