Nope. Imageine instead of ping-pong balls you had a blue squash ball (TIL: the color is important! [0]). They're squishy, and so when you poke the ball at your end, in reality you're causing it to visibly deform. It then pushes back out to a sphere, moving away from you. In doing so, it pushed into the next ball. This process of deform->reform->...deform->reform takes time, and that time is the propagation delay.

[0]: http://en.wikipedia.org/wiki/Squash_(sport)#Playing_equipmen...