study permit delay

Hello.

Due to confusions with the Canadian Embassy in Rome I have found myself without the study permit (for PhD at McGill uni in Montreal), just a week before classes start.

I have already received my CAQ, but for the study permit they additionally asked me for a police certificate (penal record) from the UK, because I did a 1-year MSc course there some years ago.

Do you think it is possible to go now to Montreal, enter the country as a plain visitor (no visitor visa is required for Greeks), so that I don't miss classes and my whole studies, and then register properly as soon as my study permit is ready (no less than 40 days)? I suppose that I will then somehow have to get out of the country and re-enter. Somebody told me that there might be a problem if I go now as a visitor, because of my study permit file they are processing! Can this be true?!

Any help or other ideas would really help!

Thank you,
Stella