It does not, no.
Cortana uses an online engine, meaning it sends what you say to Microsoft's servers for processing. This allows for greater accuracy (as Microsoft, like Google and Amazon, has a lot of data collected from its users to compare to), but at a cost of latency.
VoiceAttack uses an offline engine, which requires no connection to the internet, but uses (in case of the built-in Speech Recognition Engine) a recognition model trained only using your voice
Speech Platform 11, which can optionally be installed and used by VoiceAttack, is also offline, but uses a static model (meaning it doesn't have to/can't be trained); The trade off it that it only allows for predefined commands, not dictation.
If you're having issues with recognition, have a look at
the "VoiceAttack is listening, but what it hears is complete gibberish compared to what I said" section of this topic.