Do you live in Canada yet? If not, I can't see how CRA would get involved. (There would be nothing IRCC could ask CRA about.)
Now, if you already live in Canada, and are on a work permit, I guess there's potential they could ask your permission to contact CRA to confirm you were paying taxes while you worked here, but I'm not actually sure if that's a normal question. I don't believe it is, to the best of my knowledge.