My thought would be no it would not. As long as there is no link to that page and it is not listed as a default web page for your site. Maybe test it by putting a dummy page up and checking after your site has been crawled to see if it finds it. But I don't think it would.
I'm just wondering of if such pages could be considered doorway pages or something like cloaking. We've vanished from google after being on page 1 for our primary search terms and I'm looking for answers as to why...kind of like being dumped by someone out of the blue without any discussion/communication whatsoever.