The benefits of this when implemented correctly nonwithstanding, there's a major problem in that any implementation is highly likely to be quite flawed. See the proliferation of "health-tracking" apps that are basically quackery. With psychiatric analysis --- where the signals to track are much weakly defined than heart rate, blood pressure, etc. --- it is far too likely that apps will consistently make poor diagnoses, to the detriment of the user.
Besides, we have to start somewhere, right? If I had the opportunity, I would release it as an open-source project for other medical professionals to improve upon. I certainly wouldn't go as far as submitting it to the app store for the reasons you mentioned, i.e. the detriment to the user.
Interesting that you explicitly mention you'd do it without their knowledge/consent...
http://www.nytimes.com/2012/06/17/opinion/sunday/how-depress...