Yes, an overheating engine can be completely unrelated to the AC malfunction. BUT, a bad fan clutch can be a single cause of both, needs to be checked out. One way, with engine hot (but OFF), spin the fan by hand - there should be considerable resistance, it should not spin freely. I've replaced my fan clutch twice in 10 years, they don't last forever. This is a common malfunction often overlooked as detailed on the air-conditioning boards
http://forum.acsource.net/ or
http://www.autoacforum.com/