You should be able to board the aircraft. As to your right to enter Canada, CBSA will determine that at the point of entry. Unless you are a PR (landed) or a citizen, you don’t have the “right” to enter Canada unless CBSA allows you to.
If you are either visa-exempt or have an IM-1 visa in your current, valid, passport, you can travel to Canada for landing. You can also renew your passport now and still travel on the unexpired IM-1 visa in the old one. Take both passports with you when you travel.
Once you have PR status, you don't have to leave, so the passport validity period is not relevant.