OK, this one was a  bit weird.

Even though we had everything set up properly, I'd selected "Conservative" (instead of "Aggressive") on the Spam -> Submissions settings screen, thinking that would be a good starting point. Who knew that would prevent any definitions from ever bring created, thus no customer-specific spam definitions were created to be downloaded to our gateway. The help text indicates that two identical messages have to be received before a rule gets created, which seems reasonable for a "conservative" setting -- much of our spam is addresses to dozens or hundreds of users.

Because of very minor differences among spam messages (for example, the X-Brightmail tracker code), even if they were mostly identical, Symantec's classfiication system would never have 2 matching messages in the first place. This makes "Conservative" a pretty useless setting in my book. (assuming I'm understanding all this correctly).

So on the advice of Steve in support, I flipped the switch to "Aggressive" late yesterday and waited for some spam to roll into the quarantine overnight. I submitted it first thing this morning, and shortly after that got my first customer-specific spam definition download.