Within UI3, if I choose to export, it will dutifully create an export (mp4) file somewhere on the server. Once it's complete, I can then "download" it from the client browser. Since it may take an hour or more to create the export (from BVR to mp4 with overlay text), I'm certain that final export is stored on the server. Because once it's complete, I can download it repeatedly from the server.
For example:
The first two are being processed/queued. The remaining clips are complete. If I click on any of them, it immediately
downloads it to my client PC (without re-rendering). One is 12.4GB. It won't take many of these to eventually fill up whatever server-side storage it saves to...