Yes, school education is needed to be successful in today's world as school is a place of learning and socialization. Without the learning school can provide, one is ill-equipped for the challenges of the world, and the same can be said for the valuable socialization for which school provides opportunity.
We have all heard the story of the billionaire who dropped our of high school and started his own company. These stories are true, but they are few and far between. Having an education can open many doors that were once previously closed. Whether it is a collegiate or a trade school education, having higher learning will increase your chances of employment and advancement in today's global society.
One first needs to define what success means to them individually. Does success involve getting a good job and making lots of money? If so, then education and success would be positively correlated. But what if a persons definition of success is nontraditional and unique? Then that person could achieve their desires without ever learning anything.
Now let's explore the history of school education and how it affects people and their chances for success. The idea of secondary education (colleges) was to let people explore and learn about every possible facet there was in a subject. People nowadays think that college is necessary to get a job. The truth is that employers care whether or not you can get the job done well, regardless of if you have a piece of paper that says you can. BUT - advertising and the media would lead you to believe that college is a necessary step otherwise you'll be flipping burgers for the rest of your life. This is partly because the more students value education, the more they'll get, and the more students there are the more colleges can charge and get away with it. See the pattern? If college force you to believe that they are necessary for higher attainment, then they'll get your last dollar. The truth is that there are many skills and trades you can learn to achieve success in life. The sad part is that expensive colleges are the easiest and most straight-forward way to getting a nice job in a cubicle somewhere. So make the decision for yourself, weigh the risks and think about how you define success for yourself. College is not for everyone, yet education does help.
Back up a minute. The question asked about school education, not any kind of education. Wikipedia used to have an article showing people who did bad in school, but were still successful. The list is now somewhere on School-survival.Net. However, what about the alternatives to school? Alternatives are better explained here http://www.school-survival.net/alternatives/ but essentially, school itself is not needed for success, only the education.
But you do need education. There is so many ways to receive a education outside of the classroom. You learn throughout life. There is a school called Sudbury valley school were there is no curriculum, the facility let students live life and do what they choose. Studies show that 80% of students went to college after this school. Some people will flourish with a school environment, but lots of students will need a free learning style to succeed.