No, an observer in the slower frame would not perceive motion in the faster frame as faster-than-light (FTL) due to time dilation. Let's clarify the concept of time dilation in the context of special relativity (SR).
According to SR, the passage of time can be relative between different observers in relative motion. When two observers are moving relative to each other at significant speeds, they will measure different elapsed times for events that occur at the same location. This effect is known as time dilation.
In the scenario you described, where one clock is moving faster than another, time dilation occurs between the two frames of reference. The moving clock, as observed from the stationary frame, will appear to be running slower relative to the stationary clock. However, this does not imply that the moving clock is "exceedingly faster" from the perspective of the observer in the slower frame.
The reason is that the concept of simultaneity is also relative in special relativity. The observer in the slower frame will perceive events in the faster frame as occurring in a slower time frame, but they will not perceive them as happening faster-than-light. The perception of motion in the faster frame will still be consistent with the principles of special relativity, as no information or signal is transmitted faster-than-light.
Time dilation in special relativity is a well-established phenomenon and has been experimentally confirmed. It is a consistent aspect of the theory that allows for consistency and compatibility with other relativistic effects, such as length contraction and the relativity of simultaneity.