Will students work if there are no grades?

In my experience, yes.

I've told students that I would give a past tense quiz every Friday.  If they get 9 or 10 out of 10, the following week they don't have to take the quiz.  I obviously can't keep track of 30 students, so if someone who didn't get a perfect score doesn't come, I won't know...but if I don't notice it means that the vast majority are coming! 

The real argument here is whether if we don't grade students (that is, we give feedback, but the grade isn't entered in any official way) they will take the work seriously.  My argument is that because we assume they won't, they don't.
  
What if we take the first step in changing our attitude?