In a word, yes.
Your wifes 650 will have been authorised with an Adobe Digital Editions ID (ADE ID). So in simple terms all you need to do is authorise your reader with her ID. Also if you set up a Sony book store account also use your wifes ADE ID.
However if you're getting the T1 you may need to install the newer Reader for PC (R4PC) software, don't remove any other programs.
If done correctly you then plug in your new reader and open R4PC and authorise your reader.