In my experience, not a chance. I have been upgraded once in 20 years of business flying. That was with Qatar and only because Economy was over-booked and I was wearing a suit (which I invariably do when travelling on business). Neither my F1250 nor GATCO membership card (visible in my passport wallet when presented at check-in, not brandished about) have made a blind bit of difference.
Still, there is no harm in asking.