It sounds reasonable on the subject of establishing a false identity:
http://www.wizzywigcomics.com/?p=219
Plus, the comic could use some promotion, I think.
A quick check of the Social Security Death Index shows that no, it is not correct. Apparently anyone with a Social Security number at time of death is listed, and now days the SSN is issued pretty young. I refer you to Landon S. Smith, died 18 May 2009, age 3 months.
My guess is that if you are over forty, this trick might work, but then you have the case of an SSN of an adult suddenly becoming active for the first time, which will probably wake up a few computers in the FBI–they have heard of this, after all.
It used to work. Mechanisms were put into place to double check.
For instance, in New York, you are required to provide ID to get a copy (a driver’s license or other ID or utility bills with your name on it). Maybe other states are more lax, but it wouldn’t work in NY.