Of course it does.
All spells are on the Sublime Chord spell list, including Ranger, Paladin, Cleric, Druid, Bard, and Trapsmith.
Sublime Chords get the class features of all classes, and can wield Holy Avengers without difficulty (even if they're evil).
Each and every Sublime Chord can emulate the alignment and racial traits of every alignment and race, respectively, so they can use all those items easily.
All the gods bow to the Sublime Chord, so they have free access to every Domain-specific spell.
What good would UMD do for such a person?