The answer to your first question seems to be "maybe":
What file types can Google index?
Google can index the content of most types of pages and files. See the most common file types.
But the link to common files types are all text.
Even if you search for binary files like Windows Installers (.msi), you may get a link to a page containing the file or a direct link to the file, but Google almost certainly decides how to index it based on what is around the link on the page, rather than by downloading and deciphering the binary files' contents.
As to your main question, Google's recommended method way for checking whether the bot hit your site or not is to use a reverse-DNS lookup:
$ host 18.104.22.168
22.214.171.124.in-addr.arpa domain name pointer crawl-66-249-66-1.googlebot.com.
Keep in mind that Google's mission "is to organize the world’s information and make it universally accessible and useful." This means that they are constantly innovating, attempting to index non-text data in ways that makes it searchable. To expand on ceejayoz's idea that just because they didn't do it yesterday doesn't mean they won't do it tomorrow: Google will do everything they can to be able to it tomorrow!