I did some brief research and I'd call it a mixed bag. Looks like he definitely had a high-tech upbringing, but not necessarily a silver spoon.

Wikipedia mentions he attended Cornell and CMU (PhD).

Freakonomics blog says "He grew up in a middle-class family that lived beyond its means, in large part because his dad was about to hit it big with a computer business and the family was banking on that success. Then the success happened, and the family lived even larger — until the business suddenly fell apart, leaving everyone devastated.

Years later, James struck out on his own and he, too, struck it big."

http://freakonomics.com/2007/05/03/james-altucher-strikes-ag...