The gpu is highly parallel, which means that the 2 triangles are shaded simultaneously (as in the second triangle is started before the first is finished) and the outputs of the fragment shader are then ordered in api order and depth tested and blended.
The gpu has special circuitry to ensure the final blending step (the part that actually cares about order) happens in api order.
This means that many small triangles can still make full use of the highly parallel shading units even if they all fully overlap.
Though if your drawcall is large enough then there will be enough time between the first fragments being fully blended and their new depth written out for the early Z to see the new depth to test against.