Nope but you can do the following.
If there is a message that you really need to keep you can go to the "Messaging" application and open that message. Then when its open hold your finger on the message until a menu saying "Copy" comes up.
Choose "Copy" and then go into Microsoft Word or Microsoft Onenote and paste it in there then upload to Skydrive or use Microsoft Onenote to sync the message data that you copied from Onenote on your phone to Onenote on your computer if you have that installed.
If i have helped at all a click on the white star below would be nice thanks.
Proud to be using a Nokia Lumia 920