If this institution is totally honest, and extremely accurate in making predictions, so that obeying the laws it enforces is like one-boxing in Newcomb's problem, and somehow an institution with this predictive power has no better option than imprisonment, then yes I would be OK with it.

Please see the edit I just added to the post; it seems like my wording wasn't precise enough. I had in mind statistical treatment of large groups, not prediction of behavior on an individual basis (which I assume is the point of your analogy with Newcomb's problem).

I would also be ok with this... however by your own definition it would never happen in practice, except for extreme cases like cults or a rage virus that only infects redheads.