If I may ask a clarification about the last sentence, my understanding is that security will not start until all previous phases are completed. If this is indeed true, being stuck in criminality would actually stall the application. My criminality has been in progress for more than a year now and according to my last call security did not start yet because of this.The criminality is based on your PCCs and the biometrics you provide. The fingerprints that you provide are processed by RCMP and the result is provided to IRCC.
See https://www.canada.ca/en/immigration-refugees-citizenship/corporate/mandate/corporate-initiatives/biometrics/process-steps-2018.html
If your are exempt from biometrics, your previous biometrics will be used to process your criminality. It can take some time. Even if your criminality is in progress, it will not impact other stages, as they will continue to progress as normal.