No, Brave Search won't copy search results that users do not click on. You own your queries and clicks. Only users who opt into anonymous logging to help Brave Search send unlinkable records up, and those records are not scraped from unclicked links in SERPs.
From https://www.siliconfilter.com/hiybbprqag-google-claims-bing-... it seems Google engineers laid a trap by using IE with Bing Toolbar and Bing Search Suggestions enabled. Not clear what was gathering the data, but this article doesn't say whether the Google engineers clicked on the bogus-keyword's result link. If they did, then clickstream as you say. If they didn't, something in the IE+Bing mix scraped links from whole Google results pages.