I've found an evasive statement in the Reference Guides:
Flash Reference Guide said:
If you are using a Flash system with bilingual capability, the Information Mailbox Greeting must be recorded in both languages.
Norstar Voice Mail Reference Guide said:
If you are using a Norstar Voice Mail system with bilingual capability, the Information mailbox greeting must be recorded in both languages.
I've found a more detailed statement in the Setup and Operation Guide:
CallPilot Manager Set Up and Operation Guide said:
If CallPilot is configured as bilingual, the Information mailbox has greetings in primary and alternate languages. The rules for bilingual prompting determine which one of these caller hear. Callers press a dialpad button, depending on which country they are in, to switch to the other greeting.
My understanding is that an information mailbox will have a primary greeting and an alternate greeting if the voice mail system is bilingual. Otherwise, it will have only a primary greeting. This would explain why exsmogger doesn't have to option to record an alternate greeting, but Huffdaddy has.
My understanding is also that the alternate greeting will play when the caller is directed to the information mailbox through the automated attendant and that the caller has requested to hear the prompts from the automated attendant in the alternate language.
My understanding is also that, while the primary greeting of the information mailbox plays, the caller can press 9 to hear the alternate greeting.
So, I don't think you can choose whether the primary or alternate greeting will play, but the caller can.
Unfortunately, I don't have a voice mail on which I can test all of the above.
Any volunteers to give it a try?