I see where you are coming from, and I think this was a very well-reasoned argument.
In my opinion though, your argument prioritizes browser vendors over users, and over the competitiveness of the web vs. competing technologies like native apps.
Let's take your scenario, where somehow the Dart VM become becomes noticeably faster than Dart2JS on Google properties, to the point that users notice and get a better experience by using a browser with the Dart VM embedded.
First of all I'd mention that there is a natural competitive pressure that keeps Gmail and other Google properties "honest" so-to-speak. Chrome is far from being the only web browser, and if Gmail is perceived as being slow compared to other webmail websites, Gmail will suffer accordingly. Gmail has no incentive to cripple the speed of JS-only browsers; it has the incentive to make its app as fast as it possibly can on all major browsers.
So if hypothetical future Dart-Gmail is noticeably faster than JS Gmail, then it is likely for some fundamental reason of Dart being more optimizable, and not because of any lack of effort to make the JS version fast.
At this point, where the Dart version is faster for purely technical reasons, you say that "adopting the VM might be the only option" for other browsers. I would say first of all that it seems that there are other options, like compiling Dart to asm.js in a very peripheral part of the browser so that you wouldn't have to change your core execution VM. Given that the Dart VM is open source, this would be adding a new backend to an existing compiler (sort of like you did with Emscripten and LLVM), and not an effort comparable to developing a new compiler from scratch. It's true that this would require you to adopt some third-party code, but it would keep the Dart VM out of your browser, if not the Dart compiler.
But suppose that even that wasn't acceptable or feasible. Now the question is, is it better for (some) users to get the advantage of technology that has demonstrated that it is inherently faster, at the cost of other vendors being pressured into adopting this (standardized) technology, or is it better for all users to be equally disadvantaged, to keep the browser playing field more level?
As you surely know, browsers aren't just competing against each other, they are competing against other app platforms like native apps. If the web stays a little slower but all browser vendors are more equal, then the whole web is falling behind compared to the other, far less open and level, app platforms.
Now all of this discussion is quite premature until/unless Dart is actually distributed as part of Chrome, and the Dart VM is actually found to be noticeably faster than regular JavaScript, and Google actually uses Dart on its big properties.