No, you fly the yellow Q flag until checked in, then you remove it and fly the National flag of the country you are visiting.
Flying both at the same time would be weird..
Interesting you should mention that. In the latest BoatUS Magazine issue just out (February-March 2020), on page 32-35, article titled "Wrong answer? Try Again" about common incorrect answers to quiz questions on the BoatUS Foundation for Boating Safety free courses, choices for question #3 on pg 34, "The Q flag used for foreign port of entry means: a) We need immediate medical attention; b)Vessel is healthy, request approval to enter; c)We have no pets aboard: d)We have nothing to declare. Correct answer is B) Vessel is healthy, request approval to enter (also known as "free pratique". So technically you're right. We've cruised in Canada multiple times and once in Mexico and have never seen or been asked to fly a "Q" flag. Don't even have one on the boat. In fact in BC at least you generally check in by phone kiosk at the dock & never even see a real person. On returning to the states & checking in at Point Roberts, WA (which is peninsula separated from the US by a chunk of Canadian territory), they now require you to check in via video link chat on a CBP ROAM smart phone app.
By the way, in that same issue on pages 24 & 25 there's an article about us and our travels.
