Yes, but first, some context and reasons why to be a vegetarian.
The Torah prefers vegetarians. In fact, vegetarianism is better for Jewish observances. One does not need to wait six hours after consuming meat for dairy. Only one pair of dishes is required, save for Pesach. One also saves money on kosher meat, which, if you avoid all meat products altogether, you can’t transgress at least twenty mitzvot!
For all the above reasons I think vegetarianism is superior. It also keeps the complexion of the face intact.
Second, the Bible prefers vegetarians (Genesis 2:16). Adam and Eve are only permitted to eat plant food. This changes when humans become cruel and eat meat, resulting in the flood. After the flood, Noah is told that he may consume “Every moving creature that lives will be yours to eat” (Genesis 9:3), with the exception of a live animal (Genesis 9:4; also see Rashi on Genesis 9:3). Noah was "allowed" to eat meat as a concession to human nature. Similarly, Rambam writes that G-d does not want or need sacrifices but "allowed" them as a concession for human needs. Rav Kook wrote that the sacrifices will not continue in the messianic age and that Jews will no longer be carnivores but enjoy plant food.
Since the ideal state for the world is a state when the world will return to the state of the Garden of Edan, an ideal world will sacrifice and meat-eating is barred, it is safe to assume that the Kohen will also be a vegan.