No, the Note 3 is not going to receive the necessary firmware update to support VoLTE.
I don't know about never, but I certainly know that the Note 3 is not enabled to support VoLTE with the latest OTA. It's been confirmed by multiple sources that only the S5 and LG G2 can use VoLTE on Verizon at this time.
XDA Developers was founded by developers, for developers. It is now a valuable resource for people who want to make the most of their mobile devices, from customizing the look and feel to adding new functionality. Are you a developer?