Yes, it absolutely should. However, to do it properly, you need to exhaust the servo first. With the engine not running, press the brake half a dozen times. The servo itself (and the tubing to it) will store some vacuum for a while after shutting the engine down. The intention is that if your engine stalls, you will still get a few brake applications before you run out of servo assistance. Pressing the pedal half a dozen times without the engine running, will use up all that vacuum and the pedal should end up feeling pretty hard.
At that point, rest your foot on the brake pedal gently and start the engine, within about a second of startup, you should feel the pedal sink under the weight of your foot.
That indicates that the servo and the vacuum pump (if it's a diesel) are working correctly. However, it doesn't confirm anything about the state of the master cylinder. In days gone by, you used to be able to press the brake pedal really hard, and a slow sinking of the pedal meant either master or wheel cylinder problems. However, on some ABS-equipped Peugeots, (and other marques), I have noticed that the pedal will sink slowly under those conditions anyway - even on a new car.
Thank you for that. The principle makes sense, so I'll have a go. I'll do it on a cold start tomorrow.