Both replies are mostly correct in theory, but there is more to it. Just because a runway has ILS DOES NOT make it cabable of supporting an autoland/dual land/triple land. In theory, yes you could land there, but it most likely won't be pretty.
There are many stringent guidelines that must be adhered to to make an airport cabable of supporting autoland. placement and types of lighting, quality of the ILS signal, terrain, etc. If the airport isn't rated, you can't perform an autoland there. When I worked at KBFM, we had to do our A300,310, DC-10, & MD-11 autoland test flights at KMOB or Jacksonville, as they were the only airports rated for the landing. On the airbus, a 'dual land' is used. Meaning both autopilots are engaged simultaneously after certain criteria and flight configuration are met. The aircraft flies the localizer and glideslope to the runway while attenuating those signals to prevent erratic correction manuevering. The radio altimeter is referenced for the landing and just prior to touchdown, the nose is flared, then just after touchdown its pushed down. On autobrake equipped planes, the brakes are applied. This is a CatIII landing. Yes, the category does reference visibility, but CatII landings are approach only and incorporate just one autopilot. Usually the autopilot must be disconnected prior to 200ft AGL. (This will vary with operators) Along with autoland certification come very strict guidelines with maintenance. Hydraulic systems, rigging, leaks, avionics systems must be maintained to much higher standards. As a rule, a CATIIIB landing (virtually 0 rvr) requires operative dual vor/ils, autopilot, rad alt, etc. Everything must be working. If you'd like more info, I have numerous manuals from my autoland classes to reference.