If you don't want to see the uploading progress once recording is finished you can enable upload in background feature from Settings -> General -> Upload video in background.
If you enable this feature, and later you wish to see the progress after uploading you can click on menu icon to reveal the uploading dialog.
Another way to look at this is we only allow one recording at a time. So if you enable this feature and immediately try to start another, you won't able to instead you will see the uploading progress dialog.