Qoute from the official website (Date modified: 2018-11-07):
https://www.canada.ca/en/immigratio...rements/requirements-provincial-nominees.html
- If the province or territory selected “no” in the “Test Required", then the province or territory has determined that the applicant meets one of the exceptions and the applicant is not required to include a copy of language test results with their application for permanent residence.
Qoute from the Paper Based Application Checklist (10-2019):
https://www.canada.ca/content/dam/ircc/migration/ircc/english/pdf/kits/forms/imm5690e.pdf
You must include a copy of your language test results with your application to CIC.
From what I understand, if you didn't submit a language test during the provincial nomination, you probably don't need it. There seems a contradiction between the information from the government website and from the checklist . It is a bit confusing. I saw someone has successfully gone through the process in NOC class A without attaching the language test result but still, I am not going to take any responsibility for any outcome if you decide to submit language test or not.
The only information I can tell you about myself is I am under NOC class A and did not submit a language test, and I have not yet received an AOR so, I can't confirm it yet.