As someone who essentially took that path, I can't recommend it. My parents and I had saved up a decent college fund ($100k or so), but instead of using that to go to Top School I took the chance on a school which offered me a full ride.
Sure, I'll be graduating about ~$140k better off than most other students. But over the lifetime of a successful tech entrepreneur that amount of money is fairly meaningless. Having spent a significant amount of time on top campuses (where most of my friends went), I often regret making that decision—the caliber of students is truly higher, and the friends/networks you have from a school like Harvard will pay dividends throughout life.