Is it possible to have AppleScript tell a specific application to save unsaved documents in a preset location? generally, yes (although 'the 'default' part is undefined in most cases).
However, is it possible to have AppleScript tell *all* applications? that's a whole different story.
To do this AppleScript needs to interact with the application directly, and the application needs to support the standard 'save' command. Most do, but some apps don't save documents directly so they're going to choke on the 'save' command. Also, the 'save' command requires a location to save - there is no such 'default', so it's up to you to define where to save each document, which means your script needs to have the logic over locations, duplicate/pre-existing filenames, etc.
The logical approach would be to try the 'quit saving yes' and catch the apps that don't quit gracefully, but that doesn't work because the script will wait for the 'quit saving yes' to complete and you can't easily trap the user interaction dialog.
The other approach is to have a specific list of applications that you know will need help and target them directly - that means looking at their list of open documents, determining which ones are new and specifically saving them before issuing the quit command - a lot more work, and something that is not likely to work generically since each application's dictionary for how it handles documents is going to be different.
It's complicated by the fact that the current design standard calls for applications to gracefully save their state and restore 'unsaved' documents for later - most of Apple's apps such as Pages, Numbers, etc. do this. What you're trying to do is back-port this feature into applications that don't support the standard.
So with those caveats, it can likely be done, but it needs a lot more thought to work globally. If you can narrow the scope to a few specific apps you may have more success.