How would that even work? Search and search ads are one product.
Maybe something that would make more sense is if Google was split into two or more search engines, each of them would get a copy of the current source code and data.
We could create our own search engine, funded by showing Google Ads, today; the suggestion is that that Ads business be separate to Google's own Search business which happens to use it, but which might easily (except obviously it doesn't) use Facebook Ads or whatever instead.
(I just checked Ask Jeeves and Startpage, and they were both serving ads from Google.)