I would hate this for a number of reasons:
1. You say its not about competing against each other, but I can't fathom how else most people would interpret it. Imagine going to a panel interview, but then finding out the panel was everyone else competing against you for the job. It seems like you would actively be rewarding selfish behavior rather than group success. Any flaw or failure or mishap will immediately lead to finger pointing amongst candidates.
2. If the goal is to measure how well people work in a team, why not have them work with the team that's hiring them? The concept as proposed much less assesses someone's teamwork capability as it does assess someone's resilience against incredibly stressful hiring scenarios.
3. This doesn't sound like something someone could accomplish in a few hours, it sounds like a part-time job. This creates a seemingly biased system that will among many other things: Favor people who do your project while "on the clock" on their current job; Favor people who don't have kids or families or otherwise significant time commitments; Favor people with strong and sometimes overbearing personality traits who often gravitate toward group leader roles.
4. This sounds like a long effort for a hiring process, which can already be too long for some people. Unless the role is someone's dream job, or the compensation measures are bar none, you're going to have to provide significant benefits over your competition to keep candidates engaged, otherwise they'll just seek employment elsewhere that has the same pay, benefits, and role, minus this "trial by combat" hiring process.
5. Even with two groups of 3 candidates each, that's six people ("complete strangers") who are going to need oversight, management, and support to get anything remotely recognizable as a product delivered. How many managers or team leads are willing to take that on in addition to their normal work? How capable are your recruiters/HR people in actually supporting a robust service like this? I suspect the answer to either of those is not promising for most companies.
6. This is the kind of thing you do with your final candidate to assess all the things you're seeking to review, but doing this with a group of candidates all mashed together "thunderdome" style sounds cruel and unusual to me. Overall what you've pitched is an intern program, and its great for that, but I can't see this being functional in a hiring scenario, and I think you may run into legal issues unless you make people sign a bunch of weird documents before they even get a job offer, which could further dismay potential quality candidates.
This would, however, make a great reality show; 4/5 stars, would watch on Hulu.
In my honest opinion, what you're really looking for is a "hackathon" model with hiring capabilities built in.