I can't believe that there is any question about whether dryfire works or not. I've always incorporated far more dry fire into my practice than actual range time, both for convenience and for budgetary reasons.
I can't make it to the range every day, or even every week.
Each pull of the trigger saves me $.10, and I still get good feedback on whether my sights are moving as well as building muscle memory. Dry fire even only 100 times a day for a week, and that's almost a $70 savings in ammunition for building/reinforcing some basic, fundamental skills.
In 2013, at one of my best Nationals, I only fired about 2500 rounds in practice the whole year, and shot about 1000 rounds (not including Nationals) in matches. 2014 was probably about the same.