If you shoot a B&C buck in Mexico, is it eligible for the Boone & Crockett record book?

yes

I would have to say YES. Take Jim Shockey for example and all the record book animals he has taken from British Columbia and the Yukon. I believe B&C recognizes record animals from the entire North American Continent.

okay thanks guys.

From their website:

The Boone and Crockett Club’s big-game records keeping deals only with certain native North American big game animals. For such purposes, the southern boundary is defined as the south boundary of Mexico . Only cougar, jaguar and whitetail deer of the recognized trophy categories range south of this boundary, and only the first two reach recordable size south of Mexico. The northern limit for trophies such as polar bear and walrus is the limit of the continent and associated waters held by the United States, Canada or Greenland. Continental limits and held waters define east and west boundaries for all categories.