Not gears per se, but yes we measure internal bores routinely to less than .001" tolerances, and use bore mic's similar to the ones you showed. There are more precise, higher-resolution instruments (google air gages) but they are spendier and cover a narrower range of sizes per gage. There are also less pricier bore gages (2-pt internal micrometers or split ball and indicator types) that can be nearly as accurate as the hole mics, they also need more setup and pre- and post-calibrations to ensure the accuracy of the measurements, and can be trickier to use, and can give false readings for roundness. I have had people tell me that good cmm's can probe i.d.'s to better than .0001" resolution, but have some issues with those statements, ymmv, etc.
Something specific you want to know?