So, your chord progression is D - A - (A♯m) - Bm (b: III - VII - (♯vii) - i). Since ♯vii (A♯m) is a passing chord, we skip over it - which means, we get D - A - Bm (b: III - VII - i).
(I'm not sure why you are counting the A chord as a secondary dominant if it comes before a passing chord and actually resolves to Bm.)
Your cadence is a VII - i in B minor, because it is A - Bm. VII - i (or ♭VII - I in major) cadences are extremely common in modern popular music, and is fairly common in late Romantic and Modern classical music. The triumphant and heroic finale of Dvorak's 9th symphony, in E minor, ends with a VII43 - I (D7/A - E).
The D7/A chord has dominant function in this case. Its top note, D, is not a leading-tone if you say it is "subtonic". However, it acts more like a leading-tone; therefore, although a lot of people say a subtonic note is a whole step (major second) below the tonic while the leading-tone is half step (minor second) below, other would say it is not subtonic, but rather a "flattened leading tone". It resolves to E, which is the tonic chord that has tonic function.
Your example is basically the same. The A chord has dominant function and resolves to Bm, which is the tonic.
Now, the question is basically confusing to answer - The VII chord creates tension and resolves to the stable i chord. However, the root of the VII is a whole step below the tonic, not half. Therefore, it is either an "altered" leading-tone IAC, or "what?". So the answer to your question is: could argued to be a "yes", while it can also be a "no".