PhD Admissions Importance: Research vs. Grades
Graduate admissions committees should, in principle, be able to review all of the applications they receive in full; this is not like undergraduate admissions, where a small team may be responsible for 10,000 or 20,000 applications. That said, some of the larger graduate departments may receive several hundred applications per year, and it may be necessary to do a preliminary screening before deciding which applications will be examined in further detail. However, what gets through such a screen can vary strongly from school to school and department to department. For instance, if you're at a school whose alumni regularly go on to graduate schools and have a track record of success, that can also be a "plus" factor. If you're near the top of your class, that can also mitigate "weak" grades somewhat (because it indicates that your school resists grade inflation). 

I would hope that graduate admissions flag applications with publications listed, but it depends on whether or not the database reports that summarize applications actually can do a screen for the presence of publications. 

Your specific case, however, is unfortunately in the "no man's land"—not a clear "read no matter what," but also not an automatic "throw away," either. It is probable that you will have a tough time if you look only at "top 5" or "top 10" departments, but you should be able to get considered by many good programs.