I'm not sure you understood about updates: it's the NW.js version that does not automatically update, in neither the C3 desktop download, nor the NW.js previewer I just provided. With C3 desktop, to update the NW.js version we have to release an update, and then everyone has to go and download it again. With the NW.js previewer, there's not the step of waiting for us to release an update, so it's better: you can download updates directly from nwjs.io as soon as they're available, including nightly and minor updates. So it is an improvement over how the C3 desktop downloads worked. The C3 desktop download could update the C3 version automatically, because it's just new content on the server that gets downloaded, which I think is the source of the confusion.
There's already options to keep a Remote Preview going. You can leave the dialog open - including in its own popup window so you can move it elsewhere on your display - and then a normal preview (including pressing F5) updates Remote Preview.