Strength (maximal force) can lay a foundation for power (work/time).
Can steep hill sprints improve strength? Maybe in some untrained individuals. But for highly trained sprinters? I'm doubtful. It would be more practical for an athlete to train for maximal force production by lifting very heavy.
THEN, hills can serve as a mode of power training - aiding in the transfer of that strength to the running stride. Yeah, people will argue that hills increase ground contact time and that's not necessarily what you want when your training sprinters. BUT, sprinters will also lift heavy - where the concentric phase may last 1-3 seconds. When was the last time you saw a sprinter, in the middle of a 100m dash, plant his foot for 1-3s and push off? That doesn't happen. So, much in the same way - hill sprints may not be specific to flat-ground sprinting in terms of ground contact time, but that doesn't mean you can't trigger adaptations through their use.
Start with max sprints on very steep hills and gradually work down to shallower grades and eventually flat-ground and over-speed running. Treadmills will be hard to use for maximal sprints - you may not get a true max effort, or you may kill yourself trying.