Is your current store built with PHP? If so then it should work. You can run the Security Assist wizard to create the login, registration, profile, and forgot password pages. Then you can use the pages manager to prevent access to any pages that you need to be logged into.
Getting the orders stored in the database should be possible, but it will be a matter of working with the current shopping cart, so I can't be specific since I'm not familiar with your current system.