Someone could host emacs in virtual machines that have a bunch of real emacsen hosted with TTYs implemented in Javascript and a virtual filesystem that actually writes to Dropbox. Someone could probably make good lifestyle-business money doing that.
But why does everything need to run in the browser? You have a perfectly good OS and you can run Emacs natively and use tramp to open remote files over ssh. I do it every day, it's awesome because I'm using my local emacs configured the way I like it and I can edit files on any server that has sshd running. Problem solved.
It's even 24.1. I only have patchy wifi now so I haven't been able to finish the install yet on my tablet but it installed and ran M-x tetris just fine on my phone.
Sadly the vast majority of the C emacs core is platform-specific code, the sort of thing that emscripten would be worthless at.
That being said, a manual port of the VM and C modules is not inconceivable.