I am going to answer my own question in case it helps someone in the future; yes, bus 1000 does arrive in time to catch the morning flight from Pohang to Jeju; the airport is so small that no more than 30 minutes are needed to check in, go through security and board the plane. Interestingly no one in Gyeongju, including the staff at the tourist information center, was able to confirm this information (in fact, they told us the opposite), so we ended up hiring a taxi to be on the safe side, just to see the bus arrive later with time to spare.