ケベック州の場合は無理のようです。BC州以外でも使えることになってますが、緊急治療や救急車費用は含まれていません。
It is also important to be aware that the Ministry of Health does not subsidize fees charged for ambulance service obtained outside B.C. If you require ambulance service while in another province or outside Canada, you will charged the fees established by the out-of-province ambulance service provider. Fees range from several hundred to several thousand dollars. When purchasing additional out-of-province insurance, you are advised to obtain insurance that will cover emergency transportation while you are away and, if necessary, the cost of transportation back to B.C
私の経験ですが、以前トロントに行って流感にかかってクリニックに行ったときBCのケアカードは受け付けてくれませんでした。とりあえず自分で払って、BCに戻ってからクレームしましたがBC州の基準$35しか返ってきませんでした。実際は$150ぐらいチャージされたのですが。。。。:(
You should be aware that your provincial coverage may not pay for all the health care costs you may incur outside the province, and the difference can be substantial. For example, B.C. pays $75 (Cdn) a day for emergency in-patient hospital care, while the average cost in the U.S. often exceeds $1000 (US) a day, and can be as high as $10,000 (US) a day in intensive care. For this reason, you are strongly advised to purchase additional health insurance from a private insurer before you leave the province, whether you are going to another part of Canada or outside the country - even if you plan to be away for only a day. See Medical Care Outside B.C. for more information.
ちなみにカナダ国内旅行保険という専門の保険もあって海外旅行保険(カナダの州外もOK)よりもずっとお得ですよ。トロントの一件以来このカナダ国内旅行保険を買ってます。ケベックの時は役に立ちました。
https://www.travelunderwriters.com/corporate/TU/product/hospital-medical.htm
このwithin Canadaのものです。
http://www.healthservices.gov.bc.ca/msp/infoben/leavingbc.html#outsidebc