>>724745873 (OP)
In more ways than one.
A Palace is in a sense the unconscious self's argument against consensus morality and why the common sensibility doesn't apply to them. When a Shadow is incensed enough on some topic to completely detach from the consensus like this, it's kicked out of Mementos into "solitary"- that's what allows a Palace to form.
Following this logic, the Shadow of someone completely psychotic would almost certainly be in solitary as well, and thus have some personal location. But rather than having a few strong opinions to defend, some random, arbitrary slice of their mind would be what differed from normal. Thus, doing what the Phantom Thieves usually do to a Shadow would probably have unpredictable results at best, assuming the cognitive environment it formed was navigable in the first place.