No, and that’s why I don’t use Google or anything that isn’t encrypted and sends any data that I consider private to some datacenter. And even when I know the data is encrypted, I am careful, as anyone should be, with data leaving your computer and going to someone else’s.
“AI” is not the same thing. Why would I want my prompt to be private if I don’t want to use the result in some malicious way, be it generating CSAM or using it to cheat someone to write an article, or to generate a Deep Fake video of someone for an internet scam?
I don’t think people’s right to generate whatever image they want to jerk off to is fundamental or more important than avoiding “AI” scams and CSAM generation. There are other ways to jerk off: there’s plenty of real people porn online and also lots, lots, lots of hentai, for literally every taste. “AI” porn only has two particularities that are not satisfied by these two options, one is to generate the scene you want, and for the very remote possibility that what you have imagined has never been produced before, you can pay an artist to To do so, another is Deep Fake porn, which should be a crime, it doesn’t matter if you’re not going to publish the image.