Conditional that both people are connected to the same network (not necessarily the same server), then yes, this is possible. To do so, the person that wants to initiate the conversation would type /msg <nick of the person to chat with> <first line of message> Please note
that the above command is the general format.
Some of the other messenger services (ie: Yahoo, MSN, ICQ, AIM, etc.) will allow for multiple people to chat with each other at the same time (sort of like a conference call), rather than only one to one (like a regular phone call).
This can also be done via IRC, however it requires a person to open a room (aka channel). Most networks have few regulations regarding rooms, and some don't even have the ability to register a room.
To open a room of your own, type /join #<room name>
If the room name isn't already taken, then you'll create that room with yourself having ops status.
For more details on this, I suggest you read this sticky Finding/Creating a Channel/Server
Hope this helps.