I am not quite sure but I think that this isn't possible because of the flash-technology. All the data of your website is on the Magix-server and not on your computer. So I cannot imagine how it should be possible to use your database files. However, I am not an expert... I am just trying to help.
Yes I got it to work but there is still something a little off about my connection string. It works but not from all computers. So yes it's possible but I need some advice aswell. Did you manage to test a db?
If your question is whether Website Maker will enable you to set up your own databases and implement your own database-driven functionality, I'm afraid the answer is "no". Obviously there are ready-made functions in Website Maker (e.g. the guestbook) that rely on a database, but it's not possible e.g. to define your own database and host your own server-side code to implement a database-driven, dynamic website.