Yes and no. It all depends on where it's hosted. It also depends on where you're getting it through. One, there's live content on other websites and other platforms, but then there's the stuff that's right in Google cache. Those are two different animals in terms of getting them purged. You actually have to purge both. Caching is more or less backing the information up. When you click on Google Images, for example, you're usually seeing the cache. When you get rid of the live content, you have to get rid of the cache too—fun fact.
Now, with some companies, like Google, lawyer Carrie Goldberg helped Google write its policy to remove NCP back in 2016, I believe. I'm glad that the rest of the big tech giants, including social media like Reddit and Twitter, emulated that process. The copyright process is still easier, unfortunately. Once again, if that image is repeated 100 times, let's say, then often 100 different notices have to get sent out. You have to do it in both the search engine and on there, but here's the rub—you can get it un-cached on Google, and delisted, but that doesn't get rid of the live content.
Here's one short answer: Give my contact information, please, and I'll help your client pro bono.