You have to think about that a minute. If higher octane burns faster, turbo cars and high compression cars would be blowing engines left and right. Higher octane burns slower and helps keep this from happening.
If anything, your cat catches the unburnt fuel like it should and it evaporates or if you go for long drives, the cat gets saturated and unburnt fuel gets spit out the back....thus, loss of milage.

Higher octane isn't a cleaner gas nor a "better" quality of gas. It's a slower burning gas.