Having dined in many Michelin starred restaurants I can assure you that there is no Coke (or Pepsi) on the menus. You *may* be able to order it off menu, from the bar where its a mixer, but I am doubting that as well.
Coke is a preferred mixer as Pepsi is too sweet. So as far as mixers go they are more likely to have Coke. But its not because Coke is more high-brow, its that its the preferred mixer.
Also, if you are spending $100-$300 a plate for food and chasing it with Coke, you are doing it wrong.
Second also, Coke is a Southern company, Pepsi is for thoes damn Yankees. The South is traditionally more conservative, with lower income and less likely to travel (a huge sweeping generalization - sorry Southern FT Members)