Can a theoretical physicist win a Nobel Prize anymore?
We've now seen three Nobel prizes in physics awarded since the posting of this question (February 2016), and I think it's fair to say that the answer has proven to be an unequivocal 'yes'. So far, four out of nine physics Nobel laureates have been theorists.

The 2016 prize was awarded to three condensed matter theorists (Thouless, Haldane, and Kosterlitz) "for theoretical discoveries of topological phase transitions and topological phases of matter". The 2017 prize was awarded to Weiss, Barish, and Thorne "for decisive contributions to the LIGO detector and the observation of gravitational waves." Of these, Kip Thorne is very much a theorist, known for his work in relativity and astrophysics, and for being one of the authors of that one thick book with an apple on the cover.