I'm Lena's partner - our son goes to PSCS ( http://pscs.org/ ). I want to answer your questions, and say more about our experience of PSCS. In public school he was starting to hate learning, his time filled with curriculum being taught on a set schedule, curriculum that he had already mastered, and teachers punishing him for not conforming to their idea of who he should be and what he should be interested in.
You asked, "Would a child interested in math/engineering find success via this model?" Our son is also very oriented on math and science - the school offers challenging courses in math, chemistry, biology which he's taking and excelling in. And we've had to stretch ourselves (!) to help him do his homework. Yeah, homework? I thought this was a homework-optional school? The homework-optional was one of the things that attracted our son (and us too) in the first place. But to take the high-commitment classes, as they are called, you have to do the homework or you can't come to class. That means doing the math or chemistry or whatever on your own time. Surprisingly many kids choose to do that. I would say that is almost because they aren't being made to do it.
Engineering… PSCS has engineering classes - they have great faculty, including one who's an aeronautical engineer, designer, and builder. In 2011 their "class" (student group project) won the Northwest ASCE (American Society of Civil Engineers) Popsicle-stick bridge building competition. No small feat - they placed first in three categories (overall, strongest, and most aesthetic) against 38 schools, many of which have hundreds of students. (See http://seattleasce.org/ymf/popsiclebridge.html )
You also asked how a child-led education actually works. Yes the students do exercise a lot of leadership, choosing their own classes and projects, and how to structure their own time. But I would not say the education is exactly "child-led." The staff of adults puts a lot of work into designing a rich, nonviolent learning environment that is full of many exciting, widely varied opportunities - in academic learning, but also in civic learning, meta-learning (learning how to learn, and how to choose what to learn), arts, and how to be a whole well-rounded person. Creating that environment is leadership at a high level. PSCS is based on the Sudbury Valley School methodology which provides a basis for understanding how and why it works, you can see more about it here: http://www.sudval.com/01_abou_01.html or http://en.wikipedia.org/wiki/Sudbury_Valley_School . And here's PSCS's info on their philosophy: http://pscs.org/about-pscs/philosophy/
The staff puts a lot of attention and energy into maintaining the integrity of the community, creating a safe environment for young people to become themselves. The closest thing I can compare it to has almost been forgotten in our society - Aristotle's Lyceum ( http://en.wikipedia.org/wiki/Lyceum_(Classical) ). PSCS is chock full of learning, arts, and discourse that is engaging, exciting, and fulfilling to be a part of. Why do young people choose to learn when they can choose (for example) video games? How can they not choose learning, in this environment? The excitement draws them in. The staff are not only scholars themselves (from Yale, Duke, New England Academy of Music, etc.) but passionate learners across many subjects too and so model the behaviors that we want our young people to have in the real world.
Because students choose what to do and often how to do it - I have seen students whiz through a year of math in a few quarters, or go deep into a subject that they could never even touch in a public school.
And college? If that is what students want the school helps them get it. They know how to help students plan and present themselves to do what they want to do. As Lena said, they've had recent grads go to MIT and other great schools.
I value these concrete courses our son is pursuing, the knowledge he's gained, and the skills he is building. But I value even more that he's become comfortable in his own skin, with his own interests. And I value most that he is well on his way to becoming a life-long learner, someone who can follow his passion into whatever he is interested in without fear, someone who can learn by himself or equally well in the company of others, someone who thirsts for knowledge and personal growth and knows that nothing can stop him from being who he wants to be.
That's why I love this school. I'm happy to say more in email, over the phone, or in person, you can contact me at adamf at pobox dot com.
cheers
adam