This has been studied, I don't have the stats but it may have been in the context of Gears: users don't install new plugins lightly. Distribution deals could be bought and paid for, but that is a long road (see ChromeFrame).
Also, NPAPI is not expressive enough to enable a new programming language VM to be integrated on par with JS. Big deal, Google can write browser/OS-specific code? They tried with Gears. It's hard, and versionitis/unfrozen APIs bite hard.
Take these two points together and the NPAPI route is not going to get Dart widespread adoption outside of Chrome, any time soon. So would web developers use it if they had to compile to JS for too many visitors?
I doubt it. CoffeeScript is a transpiler and it may actually speed up code compared to writing in JS. It is popular, with slick RoR integration, but it's not taking over the world from JS.
Dart's new semantics (at least new number types, per the memo) will result in slower compiled-to-JS code, although the win may be programmer productivity. It depends on how much slower, but the first barrier with compiling is getting devs to put up with the toolchain pain.