Yes, it will be a dry flight unless you fork out the card inflight.

However, I think they might soon need to change this policy since the ATI. BA/IB are serving complimentary alcoholic drinks including liqueurs, thus I think sooner or later, those booked on these codeshare flights will start complaining to BA/IB.
Look at DL, they used to charge for everything, but now they have started serving limited wine/beer during meal service. I suspect this is due to the ATI with AF and KLM.

Cheers!