There is no problem to leave the country while in the process! My husband and I are out of the country right now and received the OWP 1 day after we left Canada!
In the OWP they give you a new visitor visa / eTA and the OWP! With your name they will see your authorizations in the system..
Please someone correct if I'm wrong! I spoke with an immigration consultant and she told me that
You were saying In the OWP they give you a new visitor visa/ ETA and the OWP? If the They means CIC, they are not, you have to apply these documents separately.