I looked at the packaging tests (thanks), but I didn't find anything useful to me.  There were a couple whose names looked promising, but they turned out to be stubs.  As far as I can tell, none of those tests actually invoke the system's C compiler, even indirectly.  They are numerous, however, so I could have overlooked something.

It occurs to me that because the extension only needs to provide one function, I could just add that to _tkinter.  That would ease testing without adding anything to the *public* API, but it seems a bit smelly to me because the point is that a user extension can trigger the bug.  Also, the added function would be accessible to programs that choose to ignore privacy convention.

Also, I am assuming that tests only need to be runnable by developers and build automatons -- i.e. someone who can and did build Python from source.  If they need also to be runnable by end users then a compiled version of any extension the tests depend upon needs to be included in binary distributions.