No, the curly quotes are available in Iowan Old Style font. I know this, because after it inserts the curly quotes in Arial Unicode MS font, I can select them and change them myself manually to Iowan Old Style font.

This document was originally created in Mac Pages, and the author of the document says that this never happens on his Mac Pages installation. In fact, when I've sent him back the document with the curly quotes in Arial Unicode MS font, he can open it on his Mac Pages and it comes out in Iowan Old Style font!

So I've decided that it's some kind of funky incompatibility between Mac Pages and Word.

I'm not going to try to chase it down anymore.