I'm not honestly sure how AWS Organizations interacts with the AWS free tier.
Rest assured, though, having lots of AWS accounts (and using AWS Organizations, their service designed to _help_ you use lots of AWS accounts) is _not_ against the terms of service.
Each account within the organization gets the limits of the free tier, just as a single account would. I think the reasoning is that if you're going to go through the hassle of setting up orgs then you're probably an enterprise user slated to take the long haul anyway.
Rest assured, though, having lots of AWS accounts (and using AWS Organizations, their service designed to _help_ you use lots of AWS accounts) is _not_ against the terms of service.