This question was asked a long time ago but remains on the unanswered queue. The answer is yes, there was a research paper studying this question. According to this answer on academia.SE, "the overall conclusion seems to be that reviewers suggested by authors provide reviews of equal quality than those selected by the editor. While they are more likely to suggest acceptance in the initial review, at later stages these suggestions seem to equalize."
Does that mean authors should aim for journals where the author gets to choose/suggest referees? I would say not! For an author, it's very worthwhile to point out that "likelihood of the paper being accepted" is the wrong metric to care about for your career, long term. If you want to maximize your likelihood of being accepted, you could publish in a vanity press journal, where you pay them to publish your work and acceptance is essentially guaranteed. But this would not be good for your career.
A better metric would be: "is this journal well-regarded by experts in my field? Will publishing there reach the audience I had in mind when I wrote the paper? Will this journal provide me with a referee report that will make my paper stronger?"
Right now, in math, essentially no journals allow the author to pick the referee. I recently wrote an answer about this, and the ways such a review process would subvert critical reasons for peer review. So, if an author came across such a journal, it would be unwise to try to publish in it, because experts might view the journal (and hence, the author, for having published in it) with suspicion due to this highly unusual referee process. Furthermore, a "soft" referee report from a friend of yours will not make your paper stronger. Others agree with me that this practice should be discouraged.
The OP is a well-respected expert in natural language processing with over 100 publications and surely knows this, so I'm aiming this answer more at a random reader interested in this kind of procedure for picking referees. In every field of science that am aware of, a large majority of experts believe it's important for referees to be chosen by editors, not authors.