First off, no. Secondly, how does giving someone your last 4 confirm your age? Social Security numbers, at least back when I got mine, were issued all over the country with different numbers. The first three indicate where your number was issued -- for instance the first three of mine are the same as everybody else who got their number where and when I did.
The rest indicated the number of numbers given out in a state or county or whatever -- the series in one area could be larger or smaller depending in the population in that area. So the last four don't prove anything about age.