Yes, my understanding is that if you’re close to spending the £10k, this will count if you upgrade from the BA basic to the BAPP card.
(edited for clarification)
ps this is backed up by Raffles’ excellent blog – headforpoints.com in which he says:
“If you decide that the BA Premium Plus card is now the better choice, you have two options. You can ring American Express and upgrade instantly (your spend to date on the free card will count towards your 2-4-1 voucher). “
This is taken from the page located at http://www.headforpoints.com/2014/06/21/british-airways-american-express-free-card-versus-premium-plus/