I've never tried this in either direction personally but the website says yes:
Arrivals lounges | Information | British Airways
Eligibility
The British Airways Arrivals Lounge in London Heathrow Terminal 5 is available for passengers who are:
- British Airways customers arriving in First or business (Club World) cabins.
- British Airways Executive Club Gold card holders arriving on a long-haul British Airways flight.
- American Airlines customers arriving in First or Business Class cabins.
- American Airlines Concierge Key card holders arriving on a long-haul American Airlines flight.
The American Airlines Arrivals Lounge at London Heathrow Terminal 3 is available for passengers who are:
- British Airways customers arriving in First or business (Club World) cabins.
- British Airways Executive Club Gold card holders arriving on a long-haul British Airways flight.
- American Airlines customers arriving in First or Business Class cabins.
- American Airlines Concierge Key card holders arriving on a long-haul American Airlines flight.