The answer is "no!".
The key to the puzzle is seeing that White can turn Black back against the stones again... into a spiral. If you haven't read ahead for the rest yet, do so before scrolling down, it's very rewarding to have read that many moves ahead!
hotcoffee: Black probably regrets not tenuki-ing after the very first white move...
Harry Fearnley: When White plays atari at _1_, why does Black not simply capture all the white stones by playing at _a_?
fractic: When White plays the white chain has two liberties left. One at a and the other one under .