Short answer: No one to read it, no one to write it. So, sadly: no.
The longer answer is less hyperbolic, but still pretty much the same. (Though I’d love to be proven wrong.)
Is there anyone to read it?
While it has been possible to buy a study bible at the BYU Bookstore, in general Mormon culture doesn’t seem that interested in the kind of informed reading that a modern study bible enables. By modern study bible, I mean something not just the more scholarly approaches such a the New Oxford Annotated Bible, or the HarperCollins Study Bible, but even the more evangelically-leaning such as the NIV Study Bible, or the ESV Study Bible. Judging from the sorts of books that seem to be popular amongst LDS today, there seems to be very little interest in the kinds of insights that scholarship brings. There is little if any evidence of much interest in really studying our scriptures in depth: witness how little attention the Reader’s Edition of the Book of Mormon has received, or how many LDS are content with the 100+ year old scholarship that Elder Talmage drew on when writing Jesus the Christ. So is there really an audience for an LDS Study Bible? I wish there were, but I’m not seeing a lot of evidence for this.
I suppose one might make an argument in favor of an LDS version of the “application” oriented bibles such as the Life Application Bible or the Faith in Action study bible, but the BYU / Institute study manuals already fill this role. (I confess that I quite like the Life Application Bible for devotional purposes.)
Who would write it?
The best study bibles — everyone has their favorites, I would include those above, plus the New Jerusalem Bible, the Jewish Study Bible, the Catholic Study Bible, the NET Bible, not to mention quite a few other excellent offerings — manage to distill centuries of scholarly thought into a cohesive, approachable set of footnotes and introductions. The authors are typically scholars who have devoted their lives to carefully weighing the various issues and arguments around textual, interpretive, thematic, and other questions, and have earned the respect of not just their peers but the wider community through their scholarship. In short, biblical studies for these authors is not a hobby, but is for the more successful writers a lifetime devotion, evidenced by commitment to learning the tools of the trade (such as the original languages) as well as immersion in what other scholars have written before them.
One might make the argument that bootstrapping is necessary: the way to build towards a serious, credible study bible would be to start with some sort of initial effort that might not tap in to all that current scholarship has to offer, but would at least open the door to a later, more complete effort. This might be true, and so some sort of initial effort could be valuable, and might even be the only path toward a “real” study bible given the LDS cultural wariness towards intellectualism. Perhaps it would be also valuable to find ways of exposing more people to the treasures that some of the current crop of study bibles offer.