Except for op-ups. Those are at the sole discretion of the GA. I remember once on a CO flight they were looking to make some room in coach by upgrading some pax. As the GA came onboard, one of the FA's said "don't pick any slobs". The GA smiled and said "definitely". Sure enough, one guy in a suit, and another dressed in polo shirt/slacks came forward.

I asked the FA while we were inflight if CO had a dress code, and she said not officially. However, picking someone by their manner of dress is not frowned upon by management.

Of course, I was wearing some pretty smooth attire as the flight as bound for Cancun. As a HP plat, my mom and I were upgraded with little asking.