I don't deny that there is a cyclic component to the loading on the seat stays but this is superimposed on a significant compressive load. I don't actually know but I suspect that this means that the seat stays never see any tensile loading. If this is the case then, as I said before, they will not suffer from fatigue crack initiation/propagation.
But you'll also get shear forces happening around (and between) the holes.
Even though you're right about the seat stays being in compression as opposed to tension (the ones that are in tension are the chainstays), the load being applied to the structure is neither constant nor always being applied from the same location. Which brings the elastic properties of the frame material into consideration. It's not a pure statics problem anymore, and that stay will fail by buckling as a result of being compromised.
Under normal usage and with no defects, you'd never see a problem. But this isn't normal usage, and those three holes will have a significant effect on the ability of the stay to withstand repeated compressive loading. And it's this, along with the shear forces around those holes, that will eventually make it eventually go "ping"
A very simple analogy would be two drinking straws - one with a pinhole in it and one that's intact. If you put the straw between your hands and push, the straw with the hole will fail more quickly / at a lower load than the one without. And it will buckle right where that hole is.