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Over at Busbud we sell a lot of Greyhound tickets. My understanding is this will maybe work in practice but you shouldn't expect it to or count on it.
It's been hard for Greyhound to have a good idea of which passengers actually show up in real-time because the drivers have validated paper tickets by hand. This is still true in many cases.
However, Greyhound is currently in the process of rolling out electronic ticket scanning. This lets them see who didn't show up to the bus and allows them resell that seat further down the line - it's part of a larger project to be more aggressive on pricing to meet demand similar to airlines.
So especially if your first bus happens to have electronic ticket scanning and the second bus happens to be popular and sold out you might have problems getting them to accept your ticket.
Some tickets are indeed refundable and changeable, these could also serve your purpose. Don't expect your seat to be held if you miss the first section though in case the bus is sold-out. You have your ticket rebooked in this case, so the system doesn't log you as a no-show and allow your seat to be resold.