There is a way to run and debug protractor web-tests in WebStorm. I just want to share this answer here
I was experiencing the same problems described by comments to S.Panfilov's answer, i.e., running protractor in WebStorm worked fine, but the debugging process got stuck somewhere.
The issue is described here. It was occurring under Mac OS X with version 0.20.1 of protractor, and node v0.10.26.
The problem is solved in version 0.22.