Is it possible to have an FMC to compute the performance and navigation without having it linked to an autopilot or flight director?
Does/did such setup exist?
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By definition an FMC / FMCS is linked to the auto flight system.
The closest thing to a standalone device is an EFB, but when it comes to fuel burn, and air data parameters, it's unable to compute the complex parameters since it's not connected to the air data computer and engines.
I've checked the history. From a 1985 Sperry ad:
Since the mid-1970s, when Sperry began developing the first true Flight Management Computer System, the term "FMCS" has been misrepresented almost as frequently as it has been misunderstood. True flight management, defined by the Sperry FMCS, integrates navigation, flight guidance and aircraft performance functions through a sophisticated computer. And in today's marketplace, the "fully-compliant system" which performs exactly as specified by its user in all modes is defined only by the Sperry FMCS.
But yes, that's an ad, so I checked further back, from 1981:
Arma boasts the first certificated airliner FMS, which is in service with the TriStars of British Airways, Delta, Gulf Air, Pan Am and Saudia. Racal-Decca Navigator is involved on the software side, and also in the support of units outside the USA. The navigation component of the FMS was derived from the earlier Mona TriStar navigation system.
That FMS was connected to the engines and autopilot, so let's check the mentioned Mona TriStar navigation system from c. 1973:
Mona is not actually a navigation system, in the sense that it does not contain any sensor equipment. Described by its designers as an automated navigation-management package, it can readily be installed in an aircraft to serve as a direct, executive link. It is capable of processing information from the existing airborne navigation system and translating the results into the autopilot and flight director signals needed to maintain en route track, height and speed.
Even that sent AP/FD commands.