When I worked forensic psych pretty much everybody who wanted to plead insanity was trying to weasel out of something horrible (time spent institutionalized NGRI is almost always waaay longer than an equivalent prison sentence so it’s only worth it if you’re going away for life anyway). Those ones would try to put on a good show on the unit but I only ever saw one of them commit hard enough (they literally faked it until they actually were mentally ill).

The people who were legit psychotic would just keep defending the psychosis as reality in increasingly bizarre ways. They’d demand to represent themselves because the court appointed lawyer kept trying to talk them into accepting treatment but noooo, they needed to make a public statement about how they’re not crazy and the gay bar really is full of alien pedos and their court date for public intoxication and indecent exposure is their big moment to let the world know.

So I guess you could. But nobody would buy it.