. The program files does not need to be synched, install mnemosyne at normal location.
On windows 7 the default location of the database is located at:
C:\Users\UserName\AppData\Roaming\Mnemosyne
On vista however, it may be located at a different location. You may choose file>open in mnemosyne and the path the dialog starts in is usually the right directory. It should contain a file called "default.db".
Once you have located the right directory, you must make a symbolic link in the dropbox directory to it. This is different than a regular link that we usually use. I used this guide:
However I wonder if it would be easier and better for you to just make a command line script that replaces changed files and adds new files once the operating system starts, since you only need to sync on the same computer.