Speaking from my own experience: no, it doesn't matter much. I went to a state school that didn't have any linguistic anthropologists when I started. When one came in, I immediately started working with him to start working on my honors thesis. There weren't any linguistic anthropology courses until my last semester, and I was done with my major classes, so I didn't officially take it (I sat in though). So what I did instead was minor in applied linguistics and worked on other stuff that could strengthen my application (letters of recommendation, excellent grades, strong statements of purpose, research, etc...).
So yes, I agree with other posters: it matters more what you do during your undergrad and after more than the "prestige" of the undergrand institution.