It may be quite expensive
I imagine this will work much the way the add-ons work with straight mileage tickets from BA. BA includes more items in taxes and fees that most other airlines do, or perhaps they do the accounting differently. Thus, if you book a transatlantic mileage itinerary with United, for example, you might have to pay $135 plus your miles, but with BA it will be more like $335 in supposed non-fare charges. I have even seen them quote $685 in taxes and fees for a "free" IAD-ABZ ticket, when a paid ticket including both fare AND taxes was actually less than that. But these fees are quirky and variable, so do call and ask.