My experience has been that the answer is (unfortunately) - sometimes.
There appear to be some cases where Google's algo does bias toward mobile-friendly and mobile-specific versions of pages, and other times where they appear to have little to no impact. It's hard to pin down when, where and why, but I suspect things like browser version on the phone, the type of device and Google's interpretation of the query and its specificity to needing a mobile version all play a role.
I will say that over the past few years, I've seen less and less mobile-specific biasing and rewarding by Google. I wrote about this here - http://www.seomoz.org/blog/whats-the-future-of-mobile-search-and-seo
Hope that helps!