so over and above the question of whether BA GGL can get access to the Chelsea lounge for AA domestic flights (any class), what do we think about BA GGL on an AA ticket (001) flying AA metal to LHR?

I am connecting in JFK on Saturday arriving with AA in J from LHR and onwards domestic J (or F as it's a 2 class). and returning on 6th, again, AA domestic J connecting to AA J TATL. I know GGL sometimes flags up as BA VIP on AA's system but wonder how that will work / show on system (BA BPs show GGL) and thus whether that will allow me access to Chelsea (on either days)?