This is really a question for the BAEC forum, but it's reasonable to guess that if AAdvantage would credit the flight as a particular fare class, then BAEC would follow the same fare class in its own AA earning table (since it receives the flight info from AA). Also please be precise whether your C is an upgrade fare class (the "cash upgrade" is miles+copay or DODU?), or C is a paid fare class (the "cash upgrade" is an upfare?). C can be either one on AA, so your scenario isn't quite clear.

Edited for clarity since posts here indicate that DODU pulls from the same inventory as instrument (e.g., miles+copay) upgrades.