They will only know the prefix for the server they are connected to. On a larger network such as Freenode, client B could be connected to another server with a different prefix length.
The prefix doesn't involve the server. The prefix that's prepended to your messages when another server passes them on to a client is ":nick!user@host " and is the same for all messages that you originate.
(On Freenode and other networks with a similar service, your hostname can be changed by services, but the client is notified of this and can update its knowledge about the prefix).
