I just searched in moma with variations of “git5 productivity” and no such study showed up. Neither LoC nor commit count is a good metric to represent a developer’s productivity.
In my personal opinion, using a git/hg like interface makes it lot easier to work on a complicated CL because you can maintain internal local branches and you can easily revert your incremental changes. That’s not at all possible in perforce. I just can’t see how git/hg interface can make anyone less productive.