Of course not! The Elizabethan English period generally celebrated at Ren Faires lasted from 1558 to 1602, the tail end of the Medieval period. Then, poor people ate bread, fish, cheese, and vegetables like turnips, carrots, and radishes. Rich people ate meat, and lots of it: venison, beef, pork, lamb. They also liked fruit like apples, plums, and pears, and fancy desserts with honey and syrups. You try finding any of that stuff at Ren Faire amongst the pizza and gelato stands.
However, those giant turkey legs do pass muster. Turkeys, a new-world food, became popular in the 1500s in Europe, after Spanish conquistadors came back with specimens from the Aztecs. They became a luxury item for the rich, and since eating with one's hands was the style of the day (forks didn't come into vogue for centuries), feasting swells might just pick up a turkey leg and gnaw away.