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I think it depends on the question of why he hasn’t go to college or is he going to. If he had an offer but dropped off then I don’t think he is a student at this moment. However, it always good to attach a letter to explain the situation, like why he is not in college. My case is a bit different than yours, my work permit was expired so I was out of status. I also attached an explanation saying why it happened.

@Lim2010 Thank you so much for gathering your thoughts on my situation. I am thinking if I should drop the idea of applying for work permit along with PR application. Since it's little complication at this time to apply for the work permit. For me As long as he could live with me here while I could apply for his PR
 
I was out of status for 8 month last year when my spouse was doing sponsorship for my PR and I just got copr today. You just need to write a explanation why you are out of status.
Hello ,

can you share your timelines?
How long it takes after temporary application number ?