Depends on what you mean by automatically. There is no connection between the database and the project and no SSMS add-in like SQL Source Control has to indicate when the database and project differ. There is the ability to do a schema compare in SSDT between the database and the project and update the project "automatically". This is how I worked when I first started with database projects. I never automated the process but I believe you could automate the schema compare and project update if you wanted to, but then you wouldn't get check-in comments and might get incomplete code.

In my opinion the best way to work with database projects is to make changes in the project first and push out to a dev environment. You can unit test in the environment using LocalDB (kind of like Express edition, but included in the SSDT install).