The best source of information on this one is the office of your County’s Assessor. So far, as an example, the Santa Clara County has been known to say that if new construction occurs only on a portion of property, then the newly constructed portion is re-assessed and assigned its own base year value. The Assessor does look at the scope of work, please check the current state of affairs before you start to have abetter idea of how your project will be treated for assessment purposes.
The Assessor will know that you have started the project, as soon as you pull the building permit. But, the Assessor is required to assess all new construction even if a building permit was not issued. Discovery of new construction occurs in a myriad of ways, such as information volunteered by the public, staff routine checks or ownership transfers.