Hi Plazz,
This is possible on some networks that allow for nick registration. DALnet comes to mind, they have a feature called memoserv that does exactly this.
Otherwise you are looking at scripting a bot to take messages for the channel(s) you use and someone to host the bot 24/7 so its always there when you connect to pick it up!
Hope this answers your question.
Best Regards,
Dizkonnekted