Without installing an IRC server on your local network, mIRC would be unable to utilize the standard IRC server connectivity and joining of channels, etc.
However, mIRC has a built-in DCC client server model that allows for direct connect between multiple mIRC clients to one mIRC client operating a DCC server.
You can find the DCC Server settings under Options --> DCC --> Server.
Once the instructor has a DCC Server running, you can initiate a connection from the student computers to the instructor computer by using the following command:
Where you specify the local IP address of the instructor's computer, followed by a comma, followed by the port number specified in the DCC Server options.