Yes it is. Download and install the Nokia_Suite on your PC. Connect the phone to PC and open Nokia Suite-->Messaging .. Then click on SYNC next to the Phone icon at the bottom..and there you go.
You can also transfer (Sync) other data like Contacts, etc.
Its advisable to Sync / Back-up your important data on regular basis..
For Back-up.. go to Tools-->Back-up ..
That does not allow you to save TexTts messges onto the PC. I was able to do it with the old Nokia suit but I am unable to do this now? Any help anyone?