Hi Doug,
Good question! There is no direct way to that from what I can tell. One function that is available is tribe_events_count_available_tickets() which will count the number of ticket for an event and display that number.
The other way to go about it would be to hide the Add to Cart buttonĀ using CSS–each event has a body class you could use to target the buttons for specific events if you didn’t want to target all of them.
Sorry I don’t have more of a concrete solution for you, but does this at least help answer your question and give you some ground to work with? Please let me know.
Cheers!
Geoff