For our application, GCKEY stated "We are processing your background check" weeks before we did biometrics.
The timeline for when background check is stated as in process seems to be all over the place from applicant to applicant, and as msb stated, sometimes they don't even show that they are doing your background check until the decision is made. If GCKEY doesn't state that background check is in progress, then there isn't really a way to tell without obtaining GCMS notes. As far as I know, the only sure way to tell if/when they have started your background check is if you order GCMS notes. It costs $5 and sometimes takes weeks to arrive but it can give you some insight into the details of where your application is at.