<p>Under what circumstances - if any - does adding programmers to a team actually speed development of an already late project?</p>

If the existing programmers are totally incompetent, then adding competent programmers may help.
I can imagine a situation where you had a very modular system, and the existing programmer(s) hadn't even
started
on a very isolated module.  In that case, assigning just that portion of the project to a new programmer might help.
Basically the Mythical Man Month references are correct, except in contrived cases like the one I made up.  Mr. Brooks did solid research to demonstrate that after a certain point, the networking and communication costs of adding new programmers to a project will outweigh any benefits you gain from their productivity.