Hello Turki,
Yes, it might lead to a problem. Because when you fill the forms for PR under CSQ, you sign a form that you intend to reside in Quebec. If they see that you're applying from another province, they might think you already moved there with no intention to come back. Also, they will ask you for all the addresses you have lived at since you were 18. So they will see that your current address is outside Quebec. So it might be tricky. Even if you put a Quebec address for mailing address, if you don't specify that your current address is in New Brunswick, and they discover it later, it might cause your trouble (because you would be concealing information from them).
The processing of the PR will take anyway at least more than 10 months. So if you intend to come back to Quebec afterwards, then it should be fine. The only issue is how you want to prove that in your application.