Yes and No.
A review is not (or at least should not be) just a list of papers in the field, it is a research paper in its own right. A review should provide some form of new structure or idea that come from reviewing the scientific output the field in question. Thus a review can be useful when either pointing at the results emerging from the review or when you wish to provide an example of where a throrough description of a field is provided. So citing a review should primaruily be for general purposes.
If you need to cite a specific detail provided by one or several references in the review you should turn to the cited articles and check them. There is, first of all, no guarantee that the citations are correct and citing something that is not correct propagates errors in publications. In addition, the cited work may not be all the relevant work supporting a point from your perspective so your sources may become biased. After all your point for writing is most likely not the same as for the one writing the review.
A review therefore has a function on its own for providing overview and synthesis which can be cited but if you need to cite details you must go to the original work and also not limit yourself to the reference list of the review.
EDIT: Just to answer the question in full: plagiarism is only if you copy the text with out quotes. If you copy the references you are not necessarily plagiarizing but you will then give the false impression that you have actually read, in part of fully, the articles concerned and that is in the realm of unethical behaviour. In the best case, it is unwise for the resons given above.