I wouldn't recommend that. If your BG checks are still in progress, it is probably because your application is stuck in criminality. Applying online won't help if your application is stuck in criminality. They will have to get the clearance from RCMP (and security clearance from CSIS) before they can set the BG checks to "Completed".
I'm sorry that your application is taking too long, I hope you see some updates soon.
Have you ordered GCMS notes to see what's going on with your application? If you haven't and plan to order notes, order it from CBSA rather than IRCC. Apparently, notes from CBSA is less redacted when compared with its IRCC counterpart.
When submitting the ATIP request, clearly explain what it is you are looking for. You can word it something like this => "Please provide GCMS notes, electronic notes of the officers, status updates and anything else related to my Citizenship grant application bearing application number CXXXXXXXX"