Fortunately, Spotify does not have that power. Annas Archive is not based in US or EU jurisdictions. They can make access for normal people a bit harder, but not shut it down.
(Edited for clarity)
(Edited for clarity)
Perhaps I misunderstood something, but according to my understanding
1. Spotify is registered in Luxembourg and has its operational headquarter in Sweden (Stockholm). Both are EU countries.
2. I guess it won't be Spotify that sues, but the individual music labels (very likely united).
But the real servers are hosted in kazachstan or russia I think. And they do not cooperate so much with EU courts.
So unless the EU installs a great firewall like china, they cannot really shut it down.
I believe the "official" AA servers only host the website + source code. The actual copyrighted content is stored by volunteers who seed the torrents.