No.
As per the promotion
A “Qualifying Booking” is a British Airways Holidays booking that meets all of the following criteria: The booking must be for a British Airways Holidays Flight + Hotel or Flight + Car or Flight + Hotel + Car package originating in the UK only and the hotel or car element of the booking must be booked for the duration of the trip. British Airways flights including codeshares and British Airways marketed and/or operated flights only. The booking must be made before 21 September 2021. Travel is for outbound departures between 9 June 2021 and 30 September 2021 inclusive (final outbound departure date is 30 September 2021). The booking must be for a stay of 5 nights or more; and must be for a minimum of 2 passengers. The participant must register their Executive Club number against their booking prior to travel.
Discussed on this thread :
https://www.flyertalk.com/forum/brit...-bookings.html