If any school district or community college district or portion of any such district is embraced within the corporate limits of a city having a charter, and the electors of the district have participated in and voted at any school election held subsequent to the adoption of and under the provisions of the charter, they shall be deemed to have submitted to be governed in all matters relating to the management of public schools within the school district or high school district or community college district as fully and to all intents and purposes as though the electors of the district had by their votes elected to be governed by the provisions of the charter.