"Caret" does work on my machine, though it took a few attempted pronunciations.
Possibly something that'd work more reliably with a custom pronunciation for "^" added to the dictionary (something to note: a custom pronunciation does not need to match the actual text or default pronunciation, E.G. you could speak "caret sign" instead)
If by "commands" you're referring to most other things on that linked page, no. Most of it is relevant only to the Windows Speech Recognition application's dictation mode (or that application in general), rather than the engine/system itself.
The first five entries in the "Commands for dictation" section do apply, as they just insert relevant characters or affect transcription directly.
Commands that manipulate existing text or perform other functions should not.
Would it be better to do something within Voice Attack for 'specialized words' that would yield a specific typed result within the Dictation {DICTATION} Token? Is that even possible.
Not sure what you mean by "within Voice Attack", but theoretically you could use the speech dictionary and custom pronunciations to try and achieve something similar.