Are there any studies proving or at least suggesting that student/teacher interaction through Classroom Response Systems actually helps the student learn? 

The companies that make the systems point to several studies that say, "Yes!".

One of the major studies that all the CRS manufacturers point to is:

Student Response Systems:
Interactivity in a Classroom Environment
Harold M. Horowitz, Ph. D., Program Director Educational Technology
IBM Corporate Education Center, Thornwood, New York 10594

Other studies which give support to enhanced learning through Classroom Response Systems can be accessed by clicking on the appropriate button below.

There seems to be little doubt over the benefit to learning by increasing classroom interaction, and the research indicates that a CRS is an effective means for providing that interaction.  CRS is a learning technology that has a positive impact on the learning environment.