There are various types of cadences that sound resolved. Classical music tends to focus on perfect cadences (V>I) and, to a lesser extent, plagal cadences (IV>I) in terms of resolved cadences. But there are other cadences that sound resolved too, and bVII can have a relatively strong "pull" to the I. Not as much as a V7 does, but it's still very much there, and it's an interesting colour
There is a cadence sometimes called the "super mario cadence" or the "lady madonna" cadence which uses this pull upwards by a tone twice, bVI > bVII > I. So the bVI pulls to the bVII, then the bVII to the I. And it doesn't even have to be in key; you're talking about Ab Bb Cm but in many cases (mario and the beatles for example) you hear this in a major context i.e. Ab major > Bb major > C major
There are a series of chord progressions that do this. The most famous is the "secondary dominant" (5 of 5 to 1) but you also see 4 of 4 to 1 and, in your case, 7 of 7 to 1.
e.g. (all examples here work with C major too)
5: Cm D7 G7 Cm
4: Cm Bb F Cm
7: Cm Ab Bb Cm
b2: Cm D Db Cm (linked example in Dm and it's Dm > F > E7 > Emaj7 > Dm)
The confusion comes that in Jazz terms we like to talk (often quite loosely) about chords with a "dominant function" aka pulling to the 1, and how flexible you can stretch that terminology depends on who you're talking to, in what situation. Often it's restricted more for chords that actually function as a substitution of a literal 5>1 (diminished chords, tritone substitutions etc.), but sometimes people do use it just to mean "any chord that pulls to a resolved 1", and in that sense you could say bVII can have a "dominant function" in a "pulls to the tonic" sense, but it's probably best to avoid that terminology in most cases.