No, no, and NO.
AO3 does not live in “the cloud” because that is other people’s computers, and other people’s computers are vulnerable to censorship.
AO3 is on its own computers. It does still have to be housed somewhere, and I suppose a determined enough hater could try to find that place and go after it, but it’s a lot harder than sending spurious complaints to Amazon or whomever going “BadWrong things are hosted on your cloud service!”
Owning the servers is a core tenet of OTW/AO3.















