Found below, see if this helps and applies to your situationHey!
If I had money for a lawyer I wouldnt be in such a rush getting my PR before the tuition deadline haha
We applied on February 2020
I came here with a study permit so I can study here for sure while waiting for my PR
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The following is from MIFI website regarding foreign students who have obtained CSQ through regular program in Quebec:
"The CSQ application is part of a process of permanent immigration as a skilled worker. The CSQ was issued to you based specifically on your capacity and your intention to enter the Québec labour market upon completion of your study program. This assumes therefore that you will not start new full-time studies in the immediate future."
Here's a link to the webpage:
https://www.immigration-quebec.gouv.qc.ca/en/immigrate-settle/students/stay-quebec/application-csq/students-quebec/after-csq.html#studies
Based on this you shouldn't start a new program of study soon after you obtain your CSQ, even though you've obtained it through the regular program. It is very likely that your CSQ will be revoked as soon as you apply for CAQ. MIDI has been acting very wierdly these days. They are being very harsh in cases where they feel applicants are misuing any loopholes, such as moving out of Quebec while waiting for PR, going to language schools which have lower standard of passing for French courses, etc. I personally wouldn't risk it.. and there are recently some cases on this forum reporting revoked CSQs for various reasons that were pretty within norm, say a year ago. I've also heard of someone almost losing her PR Visa (yes, the visa!) at the border because she had taken up a temporary position in Toronto right before she decided to land at QC-US border.
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Link to thread -
https://www.canadavisa.com/canada-immigration-discussion-board/threads/apply-study-permit-with-csq.548677/