Basically - no.

Two points really:

1) BA only upgrade when required. E.g. if economy is oversold they roll into Premium Eco. If that's over ... into Club and finally into First if necessary.

and 2) BA has a computer system that makes it's choice. It's the only thing that makes the choice and it does take status in as a factor, but by far and away it's just a small factor in a complicated system.