Joe Belfiore, corporate vice president and manager for Windows Phone Program Management, reached out on Twitter today to suggest that the WP8.1 code for the new Lumia phones, shipping with WP8.1 preinstalled, are done.
WP8.1 sw is finished for the Lumia phones that started shipping a couple weeks ago.. and we're testing the update code now. Fixes ongoing.— joebelfiore (@joebelfiore) June 11, 2014
This is good news and suggests that carriers could see the final code bits soon. Of course, it could take a while for the various manufacturers to provide final drivers and device-specific features, but rumor has it that all Lumia phones running Windows Phone 8 should be ready to update by the end of June.