Proof: I watched the HTTP stream using Webscarab after cleaning browser. There are HTTP requests, but these only ask for dependencies (packages, ...) and do not send any LaTeX source to the server (see below).
I also took a brief look at the source and the project description and using emscripten is a nice idea to bring such applications to the browser, it saves a lot rewriting overhead (programmers time!). The PDF that is generated is also generated on the client, not on the server side.
Yes, it is possible. Emscripten is quite powerful, there are ports of gnuplot, lua and various games. The github repository to the project has more information and the source files at https://github.com/manuels/pdftex.js.
The author says
It's under development and not ready to use, yet.
So we have to wait a bit how the development progresses.