Fullbright is a very prestigous and well recognized honor. I'm sure it will count for a lot, probably just as much or more than a research paper. It will also be an excellent topic in your personal statement as well as interviews. I recieved a fellowship through the US Department of Ed myself, and thats all I was asked about during every single one of my interviews. Make sure its highlighted in your primary as well as your secondaries. Tell them how it changed you, what you gave to the program, how much of an impact it had on your view of the world, etc.
Having said all of that, make sure you still do well with everything else. I don't know what your stats are/going to be for MCAT and GPA. Even Fullbright can't erase a 21 and 2.0, although I'm sure as a Fullbright, you have/will get much higher than that.
sscooterguy