Yes, if that the client does not itself automatically log messages, nor if the server does, or some log bot; some people say that IRC doesn't support server sid

Yes, if that the client does not itself automatically log messages, nor if the server does, or some log bot; some people say that IRC doesn't support server side logging, although actually it is the protocol which has no standardized way to access it, and an implementation easily can do so (you could mention the way to access it in MOTD maybe, or mention the relevant HELP topic in MOTD). (Private messages probably should not be logged by the server though, nor should messages on private channels or passworded channels, I think. Some implementations might only support logging for permanent channels anyways; I think I have once done that, but I lost it now.)