What is the lowest-speed bogey a jet fighter can intercept/escort?
There is nothing stopping a faster jet from flying a zigzag pattern behind an intercept target if the goal is to remain in close contact with it, but a large difference in airspeeds would indeed hamper some tasks like observing the cabin for signs of life or unlawful interference. So the answer is yes, a jet fighter cannot perform all the tasks involved in a typical interception of an unresponsive aircraft if the speed delta is too high.

For reference, the takeoff speeds of 4.5 generation fighters like the F-16 are in the 130 kt (240 km/h) region, while the takeoff speed of something like a C172 is around 60 kt (111 km/h). The exact weapon and fuel load of the fighter will of course have an impact, but fighters scrambled for an intercept are typically light and with an almost clean configuration. I have deliberately used takeoff speeds instead of landing speeds to factor in a margin of safety in regards to control authority; both speeds are among the lowest an aircraft can sustain, but during  close approaches to a potentially hostile aircraft, some maneuverability is required.

Still, 100+ km/h is a substantial speed gap, and has led to issues in the past:


  The Po-2 is also the only biplane credited with a documented jet-kill, as one Lockheed F-94 Starfire was lost while slowing down to 161 km/h (100 mph) – below its stall speed – during an intercept in order to engage the low flying Po-2.