Is Tiger Woods the only PGA golfer that did not have to go to Q school?

No, plenty have players have got a tour card without going to Q School, Rory McIlroy for example, he won a European Tour card from finishing high enough up the money list in tournaments he received exemptions in, them qualified for a PGA tour card from his world rank. Some players play a year on the Nationwide tour in an attempt to finish in the top 25 and win a PGA Tour card.