Two different departments to satisfy....If you are a PR or becoming a PR on arrival then you are not here temporarily. TC sets out the requirements for vehicle imports. riv.ca
From gov't website:
Importing vehicles from countries other than the United States
You cannot import a vehicle that was manufactured to meet the safety standards of a country other than the United States or Canada unless the vehicle is the following:
15 years old or older (excluding buses);
a bus manufactured before January 1, 1971; or
entering Canada temporarily.
If the vehicle you are planning to import into Canada is less than 15 years old or is a bus manufactured on or after January 1, 1971, you must prove that your vehicle qualifies for one of the above exemptions. You can find details on determining the age of a vehicle, types of temporary imports and conditions under which a vehicle may be imported temporarily by referring to the previous section called "Importing vehicles acquired in the United States."
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Second is Customs rules...Goods to follow are typically documented on B4 and subject to limitations.
Gov't d-memo
As vehicles are frequently involved, the following criteria have been developed to assist settlers in such cases:
(a) the vehicle must have been owned and possessed by the settler, in accordance with the conditions described above, prior to his or her arrival in Canada;
(b) in addition to having owned and taken possession of the vehicle abroad, the settler must have been legally entitled to operate it in the free environment abroad (e.g., have a valid driver’s licence) and have actually driven it on the open roads abroad for some distance, prior to the date on which the settler arrives in Canada. (note that a test drive using dealer licence plates or a drive only on the manufacturer’s or dealer’s premises does not qualify);
(c) the vehicle must have been licensed and insured (temporarily or otherwise), in the name of the settler, for use in the free environment abroad during the period it was used;
(d) documentary evidence is produced at the time of accounting to substantiate that the above requirements have been met;
(e) all of the remaining requirements of tariff item No. 9807.00.00 are complied with; and
(f) The vehicle is eligible for importation into Canada in accordance with Transport Canada’s laws and requirements.
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short answer....No