Make a brilliant discovery and get yourself written up in national papers for it and you'll experience some degree of fame. But for the most part—no. We're happy you find the study of the evolution of linguistics so fascinating, but you’d probably make a really boring center square.
However, plenty of anthropologists have books published, so there is always the path to literary stardom. Then, when Spielberg comes to you and offers to buy the movie rights to What We Can Learn from our Australopithecus Ancestors, you'll be an overnight sensation. You shouldn't promise your mother a seat at the Oscars just yet though.