I'm not an expert but there is a chart on the website that shows the flow of tasks..
First the sponsor is assessed for eligibility
Then the relationship is assessed to be genuine or not
Then the background check is done in which they check for criminal inadmissibility, etc
So, if they are looking at police clearances, you should be in the background check stage. After that there is only to finalize payment (if you haven't paid the last part) and then issuing of the visa.
However, it does seem the background check is the longest stage (depending on how many and which countries you've lived in or traveled to, military service, etc, etc)