It's an urban legend, fortunately:
http://www.snopes.com/business/taxes/blackssn.htm
As for the social security number being used instead of names in college admissions, it wouldn't be enough to "delete" the idea of race. People would still be able to list race-related clubs and extracurricular activities (Asian-American Student Organization, etc., and there are more subtle ones too -- we had a step team at my high school that was, as would probably be assumed, entirely African-American). Recommendations from teachers might mention race. And as Munchkin03 said, people who wanted to could always mention their "background" in the essay portion.
We can't make the process colorblind, and honestly I don't think that trying to is the right answer anyway.