Yes and yes.
Using the Airport Management Utility (part of the
Airport Mangement Tools), you can monitor what MAC addresses are connected.
To filter out their MAC addresses (or, rather, filter
in your own), open the Express's configuration in Airport Admin Utility and go to the Access Control tab.
However, MAC addresses can be spoofed so this is not a secure way to keep someone out. A better solution is to enable at least WEP and preferably WPA encryption on the Express.