It couldn't possibly rank for anything, but I set up hosting for a new domain that had been parked for a month or so and uploaded one page. Within a couple of hours after uploading that page on hosting and making the nameserver change at the registrar, along came Googlebot and the page was in the index by the next day, full title and description. Not a single, solitary link to that page from anyplace at all, and it wasn't submitted.
I think that when a domain is registered, SE's can find it. Maybe they scan whois records? But if it's just a random page thrown in a site with no links to it, I don't think it will be found without something linking to it.
Curious question though. If you email the link to someone using Gmail, will Google find it when it scans the email?