I really, really doubt it, to the point of pretty much unequivocally
saying "no". SharePoint's content is all stored in a database, not as
traditional web files, which would make the content impossible to
index.

I wasn't sure if the original question was about the google  search
appliance or Google in general, it was pretty vague. You can have a
Google search  Appliance index SharePoint out of the box. They have a
connector for it, www.google.com/enterprise/gsa/features.html.
I've never used it, but I know the functionality was there when we were
looking at them.

Actually, a google  search device can crawl  SharePoint content, since it
is accessed via a URL not database calls. However, in our IT
department we never got beyond our test environment. We needed
Kerberos authentication to do it & had trouble setting it up.

I recommend, if at all possible, to use SPS/MOSS indexing/search. In
my opinion, it is world-class.

The main blocker to using Google is the security model - SPS/MOSS are
designed to allow a crawler account to access the content _and_ store
the ACLs. This allows security trimming of the pages/content and will
only show the content the current user has access to. Google or other
web-focused crawlers tend to assume all content is the same regardless
of whom is accessing it, and therefore the indexing and/or results may
include items it shouldn't or exclude items it should based on the
crawler permissions on the SharePoint site.

Of course, if you are talking about a public SharePoint site with
anonymous access (e.g. a MOSS publishing site) this is all moot.

Yes, but why would you do that?
It doesn't extract the metadata from word docs etc