One difficulty of answering the question of whether a general counsel is a corporate officer is that the California General Corporation Law does not define "officer".  Corporations Code Section 312(a) requires a corporation to have "(1) a chairperson of the board, who may be given the title of chair of the board, chairperson of the board, chairperson, or a president or both, (2) a secretary, (3) a chief financial officer, and (4) such other officers with such titles and duties as shall be stated in the bylaws or determined by the board and as may be necessary to enable it to sign instruments and share certificates".  Under this statute a general counsel would not be a corporate officer unless specified as such in the bylaws or determined to be so by the board of directors (assuming s/he does not hold one or more of the other listed titles).  

The Delaware General Corporation Law originally required that corporations have a a president, secretary and treasurer.   As a result of subsequent amendments, a Delaware corporation must now have "such officers with such titles and duties as shall be stated in the bylaws or in a resolution of the board of directors which is not inconsistent with the bylaws and as may be necessary to enable it to sign instruments and stock certificates which comply with §§ 103(a)(2) and 158 of this title [8]".   Like California, Delaware makes no specific mention of general counsel as an officer.

However, the general counsel may be considered (deemed) to be a corporate officer under other laws and rules.  For example, FinCEN's rules implementing the Corporate Transparency Act define "senior officer" to include any individual holding the position or exercising the authority of a general counsel.  31 CFR 1010.380(f)(8).  

Etymologically speaking, an officer is someone who has the power to do work.  The term is derived from the Latin noun for "work" (opus) and the verb "to do" (facere).  For the same reason, an office is a place in which work is done.