Not necessarily, the client may have erred by being geographically located somewhere the content is censored.
But, actually, it's not a server error anyway. The client has erred by either requesting content that isn't available (404) or content the client isn't authorised to request (403).
The 5xx range is for where an action the server needs to complete has failed (upstream unreachable, parse error on a cgi script etc).
4xx is definitely the right range for this use, though it's applicability does seem a little limited. You'd use it if you've received a takedown, but an on the wire censorship mechanism is unlikely to use it