Should a review paper contain any original (previously unpublished) research?
I believe that such an approach is indeed fine. I have seen some examples of review papers in my field (example this one : http://www.sciencedirect.com/science/article/pii/S0009250904009492 ) which are by construction review papers, but which add some news results or complementary results at the end.
Furthermore, I have seen review papers where new results were produced in order to establish, say, a comparison between various modeling approaches or etc.

Consequently, yes. I believe it should not be the core of your paper nor its most important aspect, but I do find it highly pertinent to briefly add new results or non-published results in a review paper. The key word here is to introduce them briefly.