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You can invert colors using Preview's Adjust Color dialog: Open the image in Preview, then select Tools Adjust Color to open the floating color adjustment panel. On that panel, notice the sliders for Black Level and White Level.
Doing as you suggested, Word now saves the border I selected and saved in normal.dotm, but the new document page background always reverts back to white. I, like the original question poster, would like to be greeted with a black page when opening a new blank document.
To invert the image, simply move the Black Level slider all the way to the right, and the White Level slider all the way to the left. You can play with various levels of color inversion, too, by varying how much you move each slider. You may also find the results more pleasing if you lower the Brightness setting from its default level. Adobe Reader allows you to use a custom color scheme for the document background and text (already suggested by paradd0x). In v9.5, this option can be found in Prefs Accessibility.
I believe this solution is superior to simply inverting colors as in (can be installed on Mac OS X via MacPorts), as in this case you will often get a very nasty contrast: bright white on bright black. With Adobe Reader you can however choose a color scheme much nicer on the eyes, such as light grey on dark grey. Such a scheme, similar to that used by Darklooks on Linux, would help reducing eyestrain when reading PDF documents on-screen.