Management Studio Express is the client-side tool that you can use to create, setup, and administer a database that is local or on a server. If you're asking if SQL Server Express could act as that central database, the answer is, it depends. 😉 Check if Express has the features you need:

http://msdn.microsoft.com/en-US/library/ms143761(v=SQL.90).aspx

Of course for a new system, you'd probably want to consider SQL Server Express versions 2008 R2 or 2012

http://msdn.microsoft.com/en-us/library/cc645993.aspx

the newer versions allow a database up to 10 gigabytes in size instead of just 2, and will be supported longer. To synchronize an Express database with Access will require you to do the coding to update the data, and handle cases where data is modified in local Access and central SQL Server db between synchronizations.