I am not a brain scientist but the following question seems reasonable to me.
Prof. Sebastian Seung has given a TED talk named "I Am My Connectome". If I understand correctly, connectome is basically the graph whose vertices are neurons and whose edges are synapses (strictly speaking, there are many different kinds of neurons so the vertices of the graph should be colored, but let us forget it for now).
The title then appears to be a (probably intentional) oversimplification, since even though we do not understand how exactly memories are stored in the brain (and there are many different kinds of memories), things I will roughy call "electrical and chemical variables" play some role in it (so simply remembering whether there is a link or not between two neurons is not going to fly). I understand that studying these "electrical and chemical variables" is like over a half of the brain science but the exact definition is not particularly important for this question. If my understanding is correct, then one should not get overly excited about the present achievements of the Brain Preservation Foundation (the most promising one is, I think, preserving the connectome of a mammal for some time after its death using a chemical solution/freezing), since they have not shown that they can preserve any of the "electrical and chemical variables".
The question is: what information can you actually extract out of a connectome, assuming you do not know anything else about the brain? Like something about a person's health, personality, anything? The chance of them having schizophrenia? Their most likely age?