Will I be let back in to Canada like this?

[JimLarkin]

I had my BOWP approved but have not yet received the document in the mail.

This morning I got an email saying

In accordance with your work permit you have been approved an Electronic Travel Authorization (eTA). You are now authorized to travel to Canada by air.

When you travel to Canada, you will need to bring the passport you used to apply for your work permit as the eTA is electronically linked to it. Should you obtain a new passport, you will need to apply for a new eTA by visiting the following site http://www.cic.gc.ca/english/visit/eta.asp.

Airline check-in staff and the Canada Border Services Agency will have electronic access to your eTA status using your passport.

If I were to travel to the US, would I be allowed back into Canada?

Thank you