I don't think you can send a zero event and report on that - but never tryed it your neither I know the answer.
A similar case from our implementation is the search. we have a counter event for the number of search results (only set if there are any search results). and a second event which is set on each performed search (set to 1 for each search). this way we can filter on hits where "search" is 1 and "search results" does not exists - giving us the number of searches without result.
other options to get the zero results:
- set a 3rd event if search has no results
- if you have an evar (eg. search term), you can use "eVar instances" for the total searches performed.