To put an end to this story, I have my answer but in a disappointing way.

I joined the #OpenOffice.org channel on irc.freenode.net and posed the
question.  Here is the log:

[16:40] <alandd> I imported a .ppt file.  It looks great except the font
it specifies is not on my computer.  The properties dialog give the name
of the font I don't have with the statement "This font has not been
installed. The closest available font will be used."
[16:40] <alandd> Impress knows what font it picked as "closest
available" since it is using it to display the text.  How do I get
Impress to tell me the name of the font it picked?
...
[16:43] <cloph> alandd: Unfortunately there is no UI way to do so, but
easiest is to make a small sample doc, type in the name of the font into
the font-name box and then export to PDF using the builtin export.
[16:43] <cloph> Then open the PDF in a PDF viewer and display the font-info.

How's that for usability?  I need to go enter an OpenOffice.org bug.

BTW, the "closest available font" to Gill Sans is ArialMT, at least on
my computer.

Alan