After a million years of computing, I have an answer. And the answer is...
42
Ok, ok, I'm kidding. The answer is...
128
Seriously.
But if you're familiar with Hitchhiker's Guide To The Galaxy, you might well be reminded of the "answer" of 42 being announced, at which point it became clear that nobody really understood what the question was...
But I won't make you wait another million years for "the question"; I'll ask it again here, this time from the inside-out, sorta:
Q: Given an app, which has an "Icon File" in its bundle, an icns file with the full array of icns sizes in it, what is the largest icn the Dock will ever choose to display the app?
There. That's just gotta be clear now. And it should be clear that this is a detail of implementation, an obscure and arbitrary detail, a most unlikely factoid to ever appear in the Apple documentation, and a detail which can only be found by testing, moreover.
So test I did. Without volunteers, it was clearly up to Zeppenwolf The Bold to go snooping around in retail stores with a little spyware app on a thumb drive... So my answer is based on statistics and intuition, but based on what I found I am confident. And I'm posting not just because I have the answer some future googler might appreciate, but also because I came across a couple surprises.
The first surprise is a false assumption in my original post, that the maximum displayed size of the app would be different for different screens or systems. I am confident now that it is not.
In other words, the maximum displayed size of an icon in the Dock is ALWAYS 128, regardless of screen size or system.
It is very easy to test this on any particular system, of course. To test my own system, I put together a tiny ShowIconSize application. It's a Hello, World application which doesn't even say Hello, it just opens and quits. BUT it does have a very special Icon File. Instead of the same image at different resolutions, each size of icon in the icns file displays the text of what size it is. So the 512 icon has an image of the text "512", the 256 icon says "256", etc. Which of course means that you can see which size of icon the system uses in any particular place... For example, here in the Info window we see three separate sizes all used at one time:
I'm making this app available, because it's kind of a gas to take this thing for a walk around your system. Well, if you're a nerd like me it is.
FREE DEVELOPER'S TOY!!
http://www.lafn.org/~zeppenwolf/pub/ShowIconSize.app.zip
I'm getting to the second surprise, really. First, I want to point out how the ShowIconSize app appears when it's in a folder you are viewing by the finder's "View by Icon" choice. With the magnification control in the bottom of the window, you can observe the finder doing exactly what you might expect: when the icons are all really small, the finder uses the 16 size to display the app, proven by the fact that it says "16". Then as you increase magnification, it switches to the 32 size, which scales up until it gets to 64... until you finally come to rest at the 512 image.
The second surprise is that the Dock DOES NOT do this dynamic switching between icon sizes. No matter how you squish the size of the Dock through the Dock preferences, the Dock never switches down to the 64 or smaller icon sizes, it continues using the 128 size.
So, ultimately, we have the following: The Dock uses the 128 icon size and only the 128 icon size, at all times, on all systems, in all cases... (assuming a 128 is available).
And again, because I've reached this conclusion partly by examining a tiny fraction of the world's Macs... I can't logically be absolutely positive, but I'm pretty sure. But by all means, if you're interested in disproving the hypothesis, please do extend the knowledge base-- download my little app, take a screenshot... I might be a bit disappointed to see my theory go down in flames, but hey-- I'd rather have the truth.
AGENT ZEPPENWOLF
MAX DOCKTILE SIZE, REPORT COMPLETE
EYES ONLY
STARDATE 116.83.AFTER BRUNCH.4