The core process is: App Recv'd -> AOR -> SA -> AIP -> DM -> COPR (PPR, Issue PR Card, etc)
Inland, BG checks start soon after AOR and will continue usually until just after DM (up to COPR). They can run the BG check in parallel to the core process, as once they have the reports back from the BG check, they can make an assessment on Admissibility (which is part of eligibility).
In terms of notification, many report not getting notified of SA. Some report not getting document requests. So notification is a separate issue it seems.
