I know that some schools let applicants do this, but I'm having a hard time finding any HBS- or Kellogg-specific info. My advice is to call the schools and ask. They'll be able to give you a quick, straightforward answer. And don't worry about them remembering that you have low GMAT scores after you call... You don't have to tell them who you are.
About Indians being accepted with low GMAT scores, I again want to emphasize that the GMAT is the not the most important part of the app, maybe even more so for Indian applicants. It's easy to think that since Indians often have high GMAT scores, you have to have a high score, too, or else you won't get in. A better way to look at it is to think about the ways in which Indian applicants often fall short in their apps (namely, differentiating themselves with unique professional backgrounds, community service experiences, or post-MBA goals), and focus on standing out in those areas. There are no hard GMAT cut-offs, and schools often accept interesting applicants who often have a certain weakness, such as a lower GMAT score.
Scott