I definitely noticed an uptick in BA engagement when Ms F made BA Gold for the first time (her having previously been AA Platinum and BA Silver, both Oneworld Sapphire). At the time I was climbing the greasy BA pole behind her, so as a BA Silver (as far as BA knew) I was riding her coat-tails. Lots of CSD greetings, several upgrades, being moved to the 747 Upper Deck, etc. Previously our FF alliance was more towards AA, and I had the high status while Ms F had lower status, but she recently decided to pursue her own OWE status - I think wishing to have First lounge access while travelling independently may have had something to do with this
As an organisation, they certainly were putting the effort in to try to persuade their newly minted Gold member that they were a valued customer, and showing them the benefits of flying a higher class than booked.
I would certainly say that there is a difference between some Golds and others: ones that seem to be people who recently took a much stronger interest in flying BA in the middle classes (CW and WT+ mix), who therefore should have this decision reinforced by good treatment, and might be persuaded that their true place is in F get a lot of attention for a while. We'll see how this tails off in the rest of the year and next.