Very unlikely - I have had 2 operational upgrades on BA in 10 years as BA Gold - one was Economy to Premium Economy on a flight to the US shortly after I made Gold - Economy was oversold so me and my two friends got placed in PE which was nice. The other was a short-haul upgrade from economy to business, on a flight I had moved onto that same day plus my first flight after BA lost my bag so I think it was a form of "apology"...

That aside, never any upgrades. In fairness, long-haul I am often in business or first anyway so upgrades are unlikely. Allegedly the sweet spot is to book Premium Economy which gets sold out easily, then get upgraded to business. But even in that scenario, I don't know if having a Gold card really helps you.

Expect to fly economy for sure; anything else is a bonus.