Two things spring to mind here:
1. You do not earn mileage on award tickets (the airline is not going to award mileage on mileage) so no Frequent Flyer cards will be accepted. Indeed, the computer system inhibits the entering of Frequent Flyer details.
2. That having been said, there is a field for entering "FQTV EMERALD" as a General Airport comment which would ensure your status is upheld in the event of flight cancellations or other mishaps.
3. BA, as a company, recognises the importance of the repeat One World business. However, the operational staff and crew see redemption as "freebies" and, whilst our own BA Executive Club makes a free trip or a mileage up*grade as the pinnacle of achievement, US carriers in particular "queered the pitch" by diluting the value. Indeed, Another Airline was offering Platinum Status and high mileage anonymously on ebay to generate some cashflow after 09/11/02. We all got a bit cheesed off watching America West pax flying First Class (worth £8000 a do!) return from Phoenix to London for nothing - and then BA didn't get anything even approaching the Economy fare in return! Even now, quite a few of my colleagues still view mileage awards as "freeloading" - especially when the mileage has been generated on carriers away from Auntie BA!