We flew JFK-BKK on a Delta Award on Singapore Air (Raffles/Business Class).

The award covers your US travel to/from the gateway. Our travel from JFK to SFO was in BizElite. Coming home, DL made a "schedule change" and removed the LAX-SFO red-eye and re-routed us LAX-ATL-LGA. These segments were in First, as there was only 2-cabin (First/Coach) service.

We managed to get on the LAX-JFK UA red-eye, so we never took the LAX-ATL-LGA segments.

So, I guess the short answer to your question is "yes."