According to this site, no it is not yet on the Orchestrion sadly.

Which is a shame as I actually prefer it to Rise of the White Raven - Uematsu clearly took many cues from his FFVIII and IX final boss themes The Extreme and The Final Battle when he composed Tempest originally for FFXIV version 1.0, but Rise of the White Raven, although still an awesome track, just... I don't know, lacked something... (which isn't also helped by Soken just excising the lyrics and recycling it in ARR as Gaius's theme Bite of the Black Wolf). But that's just me.