tl; dr version: The voltage step propagates as a wave along the wire.

Yes, your scheme will work if you take care of termination on the line so you don't get unwanted reflections.

The speed of the voltage-step wave propagation is some fraction of the speed of light, *C*. For a low-loss coax cable, the speed will be about 0.8 *C*. For a microstrip PCB trace it's more like 0.5 ~ 0.6 *C* (about 160-170ps/inch.) 

You can take advantage of this fact to create a delay line, assuming you take care of signal integrity issues to ensure the waveforms you pick off are clean.

Here's a video with a visualization of wave propagation on a wire, unterminated and terminated: https://www.youtube.com/watch?v=ozeYaikI11g

In this video, the wire (or, more correctly, transmission line) is modeled as a distributed inductance and capacitance. With an unterminated transmission line, the wave bounces back toward the source with the same polarity (adds to the waveform as a positive step.) If it's terminated at the far end, the wave is absorbed at the end. If the line is shorted, the reflected wave is *opposite* polarity.