Yes, ftnchek is Year-2000 compliant. ftnchek has no date or time functionality of any kind, and therefore cannot have a Y2K problem.
Of course, ftnchek relies on the underlying operating system on which it runs. If the operating system fails due to a Y2K problem, then ftnchek, like all other software on that system, may become unavailable.
A related question is whether ftnchek has any features for checking Y2K compliance of Fortran programs. The answer to this, unfortunately, is no. There are no plans to add Y2K compliance checking to its capabilities.