I figured this out. The read-only state of the ConfSserver is available from the Configuration protocol, not the Managament protocol. See: Genesyslab.Platform.Configuration.Protocols.ConfServer.Requests.Security.RequestReadOperationalMode
It is interesting that you must open a connection to a conf server to determine if it is in read-only, instead of being able to obtain this information from the management layer. This seems awfully cumbersome, and I guess explains why even SCI will only show that a conf server is Started and PRIMARY, but not that it is in read-only.