In your average Psych ward isn't doing the whole detox (unless you are coming off addictions) Typically they just want to mess with your medications get you stable and tell you to follow up with your Pdoc. ECT patients are usally kept inpatient longer, but typically most people are in and out with in 7-10 days.

They don't do much blood work besides your normal stuff.

I think if anyone wants to really dig deep and look at diets and allergic reaction they will have to seek out that stuff as an out patient and find a doctor that offers that treatment. Maybe private fancy rehabs would offer that type of care, but I would not know.