No. If you want a refund you need to dispute the charge with your CC company (see the larger thread here: [CATA] Professions showing 0/0 after boost for more explanation (it’s buried in there somewhere)).
You take a few risks going that route, but I for one was successful with a charge back and as of right now have not incurred any sort of blowback from Blizzard (and why should I?).