absolutely not. You aren't dealing with static air pressure, but with a dynamic resonance device. A leak breaks or weakens the wave, like a light finger touch does on a guitar string. Test for yourself - slide any finger slightly off an open hole and as it begins to leak slightly, you'll feel more resistance. Right?
Regarding your recording - When you shift from C to clarion G, the G is flat. I emulate your sound to discover what you are doing, and I find that your lip is simply too soft. If I play the chalumeau with the same soft lip, I have to blow harder.
You need to develop a tight muscular ring around the mouthpiece (picture an o-ring slightly stretched). It supports the reed for control, but doesn't act like a soft pillow. With a good muscular ring, the reed can vibrate as designed. With a pillow-lip, the vibration is dulled and it takes more energy to blow.
If you look at an anatomy drawing of the muscles of the lips, you will see that it forms a ring. I try to always remember that when my sound goes flabby. I suggest you use a tuner as you practice this. You'll have a breakthrough in your tone throughout the instrument, as well as tuning and control. And, your lips will get a workout, but will strengthen to the task.