For immigration to Canada, is it mandatory?
As a recent immigrant, I can say that none of my official documents (personal ones) contained my permanent address. You do need to provide a mailing address, but thats only for your local consulate/visa service agent to send you your passport and confirmation of permanent residence. As my official documents didnt contain an address, it is highly improbable that IRCC will be looking to disqualify you based on two different addresses on documents. If your name is different due to marriage and such, then you need to show proof of that name change. My wife was in this situation so we submitted a public record extract showing the date of marriage and her name change. But the address was never a consideration for anyone.