Can you make MS Word display a black background with white text, but print the inverse?

On the ribbon go to "Page Layout" and then "Page Color" - select black Then on the font styles you are using, change the color to white. There's probably a way you can set this up as a default template if you want it for every document. Not sure if it will try to print it this way or not. It's not too hard to switch it all back before you print though. (revert the page background, and select all; change font color)

You could use HTML instead of word documents.

Not only is it a standard and easily viewed, but you can actually define different stylesheet for screen and printer.

Depending on your needs, you can knit the markup by hand or customize TinyMCE for your needs.
Or, as is quite common, you could use a wiki system to write your documentation, which would also give you all the features of a wiki (versioning, linking, searching, tagging etc.).

Keep your document settings for onscreen viewing as you have chosen (black background, “automatic” text color). In Word 2010, go to the File tab; select Options; select Display; go to Printing options and UNCHECK the box that says “Print background colors and images.” This will PRINT your document with black text on a white background.

Used to be you could activate a mode that gave you white text on a dark blue background, like in the DOS days. It affected only the viewing of the document; it still printed as expected. But they took that out in Office 2007, sorry.

You could in theory write a macro that changed the colors around when printing, and changed them back afterward, and then attach it to the Word document. A lot of work for little gain, though.

FYI, it takes less power to display a white screen on a modern LCD, so if that's your concern, leave it the way it is.