You can apply but there will be conflict of interest between two applications. PR shows the intention of living permanently and Study visa shows the intention to live temporarily and come back after studies (which you have to convince the VO).
If dual intent applies, you can. PR means you want to live in Canada permanently. Student permit is temporary and you have to show ties in your home country so you will return at the end of your studies.
But why do you want to study in Canada before you get your permanent resident status? Especially if your application is in progress? It will cost you twice as much or even more.
You can apply but there will be conflict of interest between two applications. PR shows the intention of living permanently and Study visa shows the intention to live temporarily and come back after studies (which you have to convince the VO).
Again, there is NO dual intent conflict for study permits in Canada. This is one of those misinformation that gets extrapolated from the US. The only thing you need to prove during the study permit application is that you wouldn't stay in the country ILLEGALLY after studies. Staying LEGALLY is not of a concern at all.