Hi,
One of the assessment the visa officers do for granting a student visa/study permit is the student has significant tie to the home country and will go back. However, it may contradict with a current PR application where the applicant wants to stay in Canada permanently.
So, there is no right answer for this situation, but you can still apply for student visa but you need to be careful in the statement of purpose while establishing tie with the home country. I am not sure if the visa officer will consider existing PR application but they can definitely see it in your profile and you should have an explanation ready for study permit application. Such as, "you want to start studying before being a PR in Canada and ask for an exception for the "tie to the home country" and you will certainly not stay in Canada without legal status" or something else.
I think PR application may affect study permit application but study permit application will not affect PR application process.
