Can I use Dictation in OS X Mountain Lion offline?

No, your speech is still sent to the Siri/Nuance servers for processing, so you can't use dictation without an Internet connection.

An alternative would be to use a third-party dictation app like Dragon Dictate.

While your machine is probably powerful enough to handle conversion (although maybe not as quickly as Apple's servers), it makes a lot of sense for Apple to keep things on their end. The software used for conversion is doubtlessly quite complex and would be a huge download. Living on their servers also means that they can push updates as frequently and quickly as they like.

No.

If you read the Dictation FAQ it's not entirely clear that you always need an active broadband internet connection, but that is how this feature works.

You cannot use it when you are not connected to Apple's servers. There are other software packages that do offline voice transcription, but that's not what is baked into Mountain Lion.

If you read up on the technology behind voice recognition and the benefits of having excessive processing power to handle colds, dialects, slang, process out background noise and other items it makes much more sense to do this server side on massive equipment rather than sending the data needed to match words to each computer and having them all do the heavy lifting autonomously.

Yes. Off-line dictation is possible since OS X 10.9, Mavericks.

Starting with OS X 10.9, you can now use dictation offline, by checking the "Enhanced Dictation" box in the Dictation system preferences.

No. It does not work offline.

And when it is online it sends personal data to Apple which in - my view - have nothing todo with speech recognition.

(By the way it makes a lot of sense NOT TO send data to Apple: You may want to use time when you are offline for dictation; rules of professional secrecy may bar you from sending data to Apple; and programs like Dragon had been perfectly capable to handle speech recognition before the arrival of the Mountain Lion.)