The client does not read from the local .rg files, otherwise, it would always see "fresh" region files, not player builds, etc...
The generation is NOT done "on the fly", you are correct; it's done then exported, and those files are sent to the clients, just like in Nav. So instead of generating region files and having to do the calculations to GENERATE the files, it already knows what to generate, and send to the client.
Hope this makes sense.
As far as how much the client has to download, I suspect that'll be the same as it is now, a minimal amount.
Now, I know you're looking for an "official" explanation, and obviously Roland isn't Kinyajuu, but bear with me anyway...
Old method: Server needed to calculate what to generate in order to make the .rg files to send to clients
New method: Server already calculated what to generate in order to make the .rg files to send to the clients
BUT, let's try the old tried and true method:
Kinyajuu, Kinyajuu, Kinyajuu, and see if we can get you that official explanation, rather than our poorly educated guesses.