FWIW, I feel the need to add here that not only are supra references are an absolute PITA to implement in software, they are also a PITA for readers (at least this one).

I have just tried this (Word 2003, Zotero 1.0.10), and it appears that you can use bookmarks as a workaround.

First, in Word, use Zotero to insert the reference: Doe (2009). Use a style with footnotes. Select the superscript of the reference (the little number of the footnote), and add a bookmark in Word (Insert > Bookmark).

When you cite Doe (2009) for the second time a few pages down, you use Zotero to add the citation as usual. In the Zotero window, add the letter X as the page number, and whatever additional words you want (e.g. the suffix "supra"). The new reference now reads something like: J. Doe, Title of Work Cited (London: Anypress, 2009), X supra.

Next, we want to replace the letter X in the reference with the actual page. In Word, click into the reference, and use shift & F9 to show the field codes. You will see something like: { ADDIN ZOTERO_ITEM {"citationItems":[{"itemID":1000,"suffix":"supra","locator":"X"}]} }. Select the letter X, and replace it with a cross-reference to the original page (Insert > Reference > Cross Reference), choosing the page number only.

Unfortunately, it seems that updating isn't quite as automatic as it should be. This is what seems to work: Still in the footnote, click into the field which shows the page number, and use shift & F9 to show the field codes. You can now click into the field code of the reference (not the cross-references page), and hit shift & F9 to reveal the normal reference. Use Zotero Refresh to get the X being replaced with the actual page number.

If the page number changes, you need to update the cross-references (F9) and then use Zotero Refresh. I know this is not quite automatic, but at least the page numbers will be sorted out by Word and therefore be correct.

Edit: rephrased, trying to make easier to understand.