I think a
demand for an upgrade would be met with the derision it deserves. Asking nicely for one might work if the loadings were right for you on the day but more likely is an automatic upgrade for a premium card holder.
Having said that, I recently flew back from the States in First on BA. There were five free seats and later I noticed Club was full so upgrades did not seem to have been offered. However, given the standard of First these days, it may have been because BA did not want to embarass itself by having someone refuse to leave Club to go into First
But that's another story....