Nick,

You an file an international company as a foreign entity in any US state without having to form a separate US entity. Typically, this process is more time-consuming and costly than forming a separate entity, and the requirements would include an equivalent of a Certificate of Good Standing issued within the past 30 business days, as well as certified copies of the formation/existence documents form the Canadian offices, and they would have to then be certified by the U.S. Embassy in Canada to be accepted by the U.S. state offices.

You can obtain an EIN for your business whether it is registered in Canada or the United States, and use this EIN to open a company bank account (but you need to supply more documents, such as company registration documents and personal identification and address verification material).