I do not know whether citing the reviewer helps, but I know that the obsession with impact factors has lead journals to ask for citing articles which appeared in the same journal. I had two rejections for "not enough citations", and a friend had an article rejected because "the topic is not within the scope of this journal, which can be seen by the fact that none of the citations appeared in this journal".
I highly doubt there can be any study on this, because statistics on something that's suppose to be anonymous will be hard to come by.
I can say anecdotally that:
If the reviewer says "you should cite these papers" (which are written by him), and the author does it, then indeed the reviewer is more likely to recommend acceptance. However few reviewers are so blatant as to return a review that's simply "you should cite these papers". They'll usually recommend other things as well, and it's reasonable that with those other things done the paper is acceptable anyway.
There are also reviewers who recommend rejection even though they're cited. I know this because I've searched for reviewers from the references cited before, and some of them recommend rejection anyway. Of course when this happens the authors never know about it.
I remember reading about a paper where the referee said "my group's work was cited but I still don't understand what the authors are saying", which was actually a fair report since the paper was nonsense (I don't remember if it was generated by SCIgen or was a very badly written theoretical physics paper with no real content); however I can't find it now.
I was thinking of the same question. I experienced submitting a paper in the Journal X and later on was recommended by the editor to submit the paper on Journal Y (because it doesn't fit to the scope of the journal), where he is the subject editor. I cited most of his recent work on the paper knowing he is the editor in chief of Journal X. Later on, the paper was reviewed and accepted with minor revisions in Journal Y. The review was rigorous but 'soft'. However, the chance of getting accepted larly relies on the paper's quality but citing the reviewer's or editor's work means you know who are the people working on your field, you know what knowledge is exist, hence, your paper is reliable