Earlier quoted context omitted.
The URLs don't need to be posted online. Some browsers (Chrome, possibly Firefox with Safe Browsing mode, very likely any browser with a Google Toolbar installed) send visited URLs to Google and they will be indexed. I don't know if this is officially documented by Google, but several people have reported seeing this while testing new/beta websites that weren't published or linked anywhere.
I'm not sure either, but I doubt that Chrome or any of the badware-stopping features that are built in to it cause the URLs they're checking to be indexed. I'd be even more surprised if Firefox did this. If you've got the toolbar installed though, I'd be less surprised if they tried crawling or indexing URLs you go to. EDIT: It looks like they've explicitly said the toolbar does not cause things to appear in search r…
I read this too after posting, but I'm skeptical. It wouldn't be the first time they claimed to not do things they later admitted doing ... The rationale being that search engines need a way to discover new URLs quickly and keep ahead of the competition (indexing speed and breadth).
I'd also like to know what exactly Google Desktop Search does with URLs it finds.