> Will a perceived lack of trust cripple the effectiveness of the program?"
Yes. Next obvious question?
The program you describe is highly unethical and you should have nothing to do with it. If you were ever to apply to me for a job and you told me about this program, I would treat you like you're radioactive.
The program you describe will succeed only in setting up an adversarial relationship between the students and the school, and teach them that adults are not to be trusted. Further, you're trying to extend the school's ability to censor and monitor into the home, where it doesn't belong. You are planning to MANDATE that students use a CENSORED, SPIED UPON computer IN THEIR HOMES. THE SCHOOL IS A BRANCH OF THE GOVERNMENT. WHEN A GOVERNMENT ORGANIZATION IS SPYING AND CENSORING IN THE HOME, THIS COUNTRY AND EVERYTHING IT WAS FOUNDED ON HAVE GONE TO HELL.
How do you think you're going to teach kids about freedom of speech and the right to privacy when you're carefully violating both?
If I were a parent, I would forbid the computer from entering my home, and if you tried to enforce it, I'd sue the school.