Yes. You can copy or save the text chat from a meeting as long as the host has not ended the meeting yet.
There are also several different file formats the text can be saved to, depending on your needs.

Simply right-click on the chat window and select an option from the chat menu.
Note: If you have some of the text selected in the chat window, there are additional options that are available in the menu (See below).

The Chat menu when NO text is selected in the chat window.

The Chat menu when text IS selected in the chat window.

You can also save the text in several file formats, such as PDF, HTML or plain text from the Save As... dialogue as shown below.