I responded to another comment in this thread with the details, but in summary, no.

See this previous discussion: https://news.ycombinator.com/item?id=46708678

When that news first went out, the article[0] I read at the time said that Kagi does purchase some of its indexing from Google.

[0] https://www.404media.co/email/4650b997-7cc3-4578-834c-7e663e...