Yes, you can set up a database on one site / server and connect to it from another site/server. You can then pull whatever information you want from the DB.
Code:
$dbName='NameOfDatabase';
$dbUser='DatabaseUser';
$dbPass='DatabasePassword';
$dbServer='Server/Host';
mysql_connect ($dbServer, $dbUser, $dbPass) or die ('Error connecting to the database because: ' . mysql_error());
Just set the $dbServer to where the db is hosted.
-Bob