No, you can't use logic that depends on multiple scans or the passage of time in a Fault Routine.
It is pretty common to have an IO module connection failure cause a Major Fault in ControlLogix, since some I/O devices are critical to the control process. Sometimes that default setting causes faults that the system designer did not intend.
What is the application where you need a time delay ? Are you trying to react to an I/O module connection failure, or a detected condition like an overload, short-circuit, or open-wire fault ?