In theory, as a Star Alliance Gold traveler you are entitled to priority tagging of your checked luggage at check-in for all *A flights. If you see that it does not occur automatically, you should specifically ask that the "orange arrow" be placed adhesively in your UA-generated, barcoded bag tag.

In practice, fat lot of good it does. Last week I flew United Business to Australia and my one checked suitcase had the orange arrow. Not only was my bag not first off the plane, it was never off the plane. This sank in as I stood there, alone, like a moron an hour after we landed. The bag somehow got lost on the nonstop flight from SFO to SYD, and only turned up 2 days later in Perth.

The only priority bag is one that's carried on.