It seems like the only short-term risk is that I could have unforeseen medical expenses that they refuse to reimburse for one reason or another. In my particular situation, I may just try it for two months to get me to 2017 and see what happens. If I like what I see, I may walk away from standard medical insurance completely.
One other thing, and I'm not sure if the other ministries have similar requirements, CHM did require an actively Christian life for membership. That means meeting regularly and faithfully with other Christians to fulfill ministry (church) and be engaged in furthering Christianity. At a minimum, being a member, or a regular participant, in a local church and in good standing.
I always felt a little guilty since, during my membership, I became disillusioned with the large church I had been attending, and began church shopping, so I didn't have a regular congregation to call my own for a while. But the association makes sense. These ministries want practicing, orthodox Christians who support each other. This contributes to health and reduces health costs.