How can I check if a computer is configured to use WSUS?

As it is part of a domain, it is most likely done through group policy, you can go to the desktop as an administrator and open up the Group Policy Editor (Go to Run and type MMC, then go to File > Add / Remove Snapin) and find Group Policy.

Take a look under Computer Configuration > Administrative Templates > Windows Components > Windows Update.

If you are not using group policy, just take a look directly at the registry key:

HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\WindowsUpdate

You should see the keys WUServer and WUStatusServer which should have the the locations of the specific servers.

There are far too many keys and entries for me to write, but if you are interested, Technet have an excellent article on all of them.