Similar thing happened to me once, but in reverse order. Arriving in ATL from a transatlantic flight upgraded with miles, I missed the domestic portion of my itinerary that was also upgraded using miles. So the agent put me on the next flight and the class on my boarding pass showed as "F" (full-fare first class) as opposed to V or O class (can't remember which is for first upgrade w/ miles). And I even got double MQMs for that flight back when full-fare First got 2xMQM.

So my feeling is that as long as there are seats available in Business, the agent could assign them to you as "J" class.