You're correct, it will never be accurate as closing the web client will remove their presence, however I thought you were setting this up at the minute and therefore you would be able to see who logged in within a XX amount of time window. As I mentioned previously there is no native way to do this.
The idea with the reports was to give you a hint at best, but there won't be any accurate result as if the extension is a chat only extension, it'll display 0 calls in the report too.