Not if you are using Yahoo Messenger, the full version, because the message archives are stored locally on your computer. You cannot access them from another computer.
Now if you were using Yahoo Messenger for the Web, it does have a message history feature that when enabled, stores message history on the Yahoo Servers. You can then access it from any computer. I have had problems getting it to work properly but not everybody has this problem.
Please note that at this time there is no chat history or archiving feature in the Yahoo! Mail chat. The most you can do if you want to save a chat session is if you are using the All-New Yahoo! Mail is to turn the chat into an email and send it to yourself. This feature is not available in Yahoo! Classic Mail.
http://help.yahoo.com/l/us/yahoo/mail/yahoomail/chat/chat-08.html;_ylt=AsrVn_4vjpX3HmYC38YUdkhq5yN4