Well...given Seeu's past and his current actions, I would give a tentative 'yes' towards Seeu being insane. But he isn't really 'mad' in the sense that he goes off and kills people; it's quite the contrary. Seeu is broken. In tankouban four, when Kaguya begins to talk to him about Kagami, Seeu passes out.
According to the sage Meshie Laracott, Seeu's body shuts down when he is forced to confront the past.
"This man is broken, Kaguya. His head and his reasoning are normal...but you've seen his emotions... When he experiences a large emotional swing, his brittle, fragile spirit just breaks. In defense of itself, his body shuts down to avoid any further stimuli from the outside."
So...while Seeu is certainly unbalanced, I don't really think that he's insane. He is also incapable of touching other people; he literally cannot close the distance to another person.
He's very quiet and has very few social skills. But still - Seeu isn't quite mad. While it may seem that way to others sometimes, Seeu obviously has a plan and knows what he is doing.
Never having touched another person could certainly drive a someone insane; and Seeu, when he was younger (and still now, for all we know), used to wreck the palace (and himself, really) in a sort of fit.
So Seeu is perhaps "out of it," but "insane" is a little bit strong to use on Seeu.
"The mad prince with the silver sickle lived in a hidden place on the remains of a tomb..."