Are there any studies on how lecturer review sites such as Rate Your Lecturer affect student choices?
This is necessarily incomplete, but I do recall a few studies on the correlation between ratemyprofessor.com rankings and student evaluations. Two such studies are:


Hotness and Quality
Student evaluations and RMP


These are disappointingly old though (2006/2007)

There's a more recent study from 2011:


Researchers and RMP


As for other studies, your google is as good as mine :)