Yes, almost exactly. A 60 mm cube at 60 mm/s and 20% infill takes 3.95 hours at 0.2 mm and 7.9 hours at 0.1 mm.
The extruded volume is identical — 57,824 mm³ either way. You are not printing more plastic. You are printing the same plastic through half the flow.
Why the doubling is so clean
Flow is layer height × line width × speed. Halve the layer height at a fixed speed and the flow halves: 5.4 mm³/s becomes 2.7. The same volume at half the rate takes twice as long.
The layer count doubles too — 300 becomes 600 — which doubles the per-layer overhead of Z moves and seam positioning. Both terms move the same way, which is why the relationship is so nearly linear.
Going the other way is not symmetrical
Raise the cube to 0.3 mm layers and it takes 2.658 hours, not the 1.98 that a strict inverse would give. Two things get in the way: the solid top and bottom skins are defined by thickness rather than layer count, so they do not thin out, and the extruded volume actually rises slightly to 58,366 mm³ because thicker layers pack the geometry differently.
Thicker layers still pay, and they pay a lot. They just do not pay quite as much as the arithmetic suggests.
Can you claw the time back with speed?
Partly. Doubling the commanded speed to 120 mm/s at 0.1 mm brings the cube back to 4.033 hours — close to the original, and only because 0.1 mm layers demand so little flow that there is headroom. The requested 5.4 mm³/s sits well under the 16.5 mm³/s ceiling.
Try the same trick at 0.3 mm and it fails, because the flow demand is already near the ceiling and the printer simply slows itself down.
Is it worth it?
For a display model, sometimes. For a functional part, essentially never — fine layers do nothing measurable for strength, and layer adhesion is governed by temperature and line width rather than by how many welds you stack up.
Run the same geometry twice at two layer heights in the print time estimator to see the cost on your own machine. Whether finer layers buy anything mechanical is answered in the layer height and strength guide.