Whelp, this weekend I'll be in the office listening to recordings of my students and doing word counts to measure English ability and confidence.
It's too early for a definitive conclusion, but it looks like using the Socratic Method in a beginner English class won't improve your students' language abilities directly. But more indirectly it can improve confidence and lessen anxiety, which are important goals in a beginner class.
But we won't know for sure until all of this data gets crunched. And between pre and post surveys, experimental and control studies, and pre and post project studies involving almost 500 students, there's a metric f-ton of data to crunch.