IMO, using background color is acceptable as long as it is used sparingly for visual effect. You almost certainly should not use white-on-black for the body text of an entire book.
One or two special pages in a book, however, are unlikely to annoy anyone.
I would also suggest setting !important on both the background and the color properties as a clear indication to the reading system that this is *not* ordinary body text that it can re-style at will without breaking things.
Even then, you might have a few buggy readers (Nook on iOS, I'm looking at you) that "helpfully" try to set the text color to black but don't change the background (resulting in black-on-black text). At least in the case of Nook on iOS, you can fix this by enabling publisher styles (and why that mode is not the default, I will never understand), but it is worth keeping in mind.
In iBooks on iPhone/iPad, inverted text behaves exactly as you would expect. Likewise in every other reader I tried except for Nook. *ahem*