Looks like you can. Mine sync'd by setting the download location then in the advanced tab, clicking on the Reload button. This can be done by clicking on you user name drop down and selecting settings.
NOTE: I am using version 5.5.1.1028 of Amazon Music Player.
Goto Settings
Click on the user and select settings.
Select download location
For this you need to map a network drive to the NAS. I am sure this used to work in the previous version of the Amazon Music Player - where you could just type in the path - now it is read only. Given I haven't setup my Network at home, the computers didn't show up for me under the Network item when browsing.
Reload music information
Click on the Start Reload button.
Sync'd
Now what is downloaded already should have the correct icon.
