I saw some similar cases, people tended to apply for Study permit first then PR and it seems working fine… see the below response:
If I should apply for my Study Permit before my family submits application for PR? -
YES you can ( My friend has done the same thing) Now we are doing the same thing for Fall Intake…(Got ITA too) File PR app after study permit application
2. When I apply for my Study Permit, do I need to mention about ITA and/or express entry profile, even though technically, I have not applied for PR?
Yes you can attach the copy of ITA and mention about the dual intentions
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Will it be wrong on my part to keep quiet about my ITA/Express entry?
Yes it is wrong, they can actually find out from CIC
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Is my upfront medical type: Worker, linked to my Express Entry application (Starting with"E")?
You can use the same medicals though remarks may be different.
Tests are same for both worker, dependent and Exp Entry.
The test date should be within 6 months on the date of application. (Thats it)
If you are concerned with legality, to an agent and see professional advise.