The micrometers that I have seen use a capacitative encoder like the digital caliper but circular, not an opto or magnetically coupled encoder which would use a lot more power. The stator has many electrodes that capacitativly couple to a rotating pcb .
With this scheme the counting circuits are powered all of the time so that the device "remembers" the number of turns from zero to save the user having to mechanically reset the micrometer to the anvils together position.
So turning the device on only powers up the display but it will draw a very small current when switched off, Mitutoyo's have a very low standby current compaired with some other brands.
Billy.