If anyone is planning on traveling abroad, here has been my experience:
I’ve went to the US twice in less than two months for business trips (around 15 days each), and on each time when I returned, the Canadian customs officers asked for my passport with the eTA + OWP, the purpose of my trip, where I work and what kind of Work Permit I had. Both times I told them I got the OWP after applying for PR. I did not say it was from the Family Application (didn’t see the need to) and they’ve release me in less than 30 seconds.
At least for business trips, going abroad seems to be okay.