Can my wife apply for study permit while we are applying for immigration?

I am working in Canada and my wife is working in China. We are applying for skilled worker together and we plan to submit the application soon. Meanwhile, my wife is also applying for schools in Canada. Does my wife's application for both immigration and school in Canada conflict each other?

If my wife gets accepted by one school, she will need to apply for study permit. I remember that one needs to convince the immigration office that one does not have immigration intention while applying for study permit. So I am worried that her application to immigration might prevent her from getting a study permit.

The application for skilled worker will take over 10 monthes at least, which is a bit long for us. That's why she wants to come to Canada on a study permit first. What do you guys suggest?

Thank you very much.