Does the Zenith have anything to do with the read-out of an IRU accelerometer?
Good question.

Another name for the "position of the Zenith" would be the gravity vector. Which for an aircraft is always down (shortest distance to reunite with terra firma).


  Note that it is necessary to subtract acceleration due to gravity from the vertical channel before performing the integration.—An introduction to inertial navigation


So the answer is yes, the acceleration due to the gravity vector is corrected.

Check the PDF for a detailed description and equations.