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At mile marker one I place one baloon, at mile marker two I place two baloons, and so on, I pop all the balloons at once. The pressure readings are going to differ for some time after. No matter what scale you use this is the way it works.

We're talking about just a bit more air than that, and hence, "some time after" is going to be quite a bit shorter than with your balloons. After you open your door, there is going to be some point where the pressure at the bottom of the tube is still zero - no air has reached the bottom yet - but is something else, some non-zero pressure, higher up the tube.

Now, if you happen to be standing in the middle of the tube, there is going to be a point where the pressure around you increases from zero to something, and rather rapidly too. The farther away from the mouth of the tube you're standing, the longer you're going to have to wait for that to happen, because the air has to travel down at the tunnel to get to you. But it will happen, because that air is coming, whether you paid attention to Boyle's law or not.

Well, you're meandering argument has finally found its way into my court. Thank you for agreeing with me, even if belatedly.

My original point was that pressure rise would be linear, not instant. Thus the onset of load to the vehicle would be somewhat cushioned.

It was never my point that simply opening the end of the tube and letting air rush in was a "great idea", just that it would also result in a linear onset of pressure. However, the turbulent airflow near the muzzle might be a problem. Mr. Boyle's law certainly states that increasing volume decreases pressure, so I think I've got that one covered. The Bernoulli effect supports my argument, but only as far as pressure goes, when in actuality I'm concerned about the mass of the gas more than its static pressure. As the gas would be moving quickly, its measured static pressure would be lower than its mass would create under, well, static conditions. As the vehicle hitting it would create a whole new dynamic, it would be unfair of me to use Bernoulli as my supporting element. However, Bernoulli certainly would NOT support your original posts, which were maintaining a solid flow of air at 1 atmosphere, as the leading edge of the wave would be moving the fastest, with incidentally ever decreasing mass. Why? Because gas molecules bounce around at random. They turn when they hit something including each other.
Your point that no matter what it would eventually reach equilibrium wasn't ever contested. However, if the door were to open for even ten seconds (an eternity for the given dynamics) the air that rushed in would have the entire 100 mile tube to fill. Under your original premise a wave of air (unaffected by the flow dynamics in its wake) would be a 1 atmosphere puff that went all the way to the end, and then I assume bounce back.
Completely academic however, as letting atmospheric oxygen into a container where it would get so greatly compressed would be a bad idea. Bleeding nitrogen in as I suggested, before opening the door would be much better.