Complex question
Caveat: I don't work for Google and the precise workings of the canonical element in Google's algorithm is mostly educated speculation.
The answer is somewhere in-between yes and no. That's because the canonical element means that URL B is treated as URL A. In that sense it really shouldn't pass any direct link authority.
But(!) now let's complicate things. Let's point some links at URL B. (and not at URL A) In theory, those links are then canonicalized to URL A, and that equity passes to your site (yeah!)
So it's not a direct influence, but you can in theory gain link equity from canonicalized versions of URLs that point to your site.