Yes, but you cannot be playing for AYSO or a club team at the same time that you are playing for a high school team. Therefore, the AYSO season is carefully set up so that the Upper Divisions (U16 & U19) are finished in mid-November before the winter high school soccer season starts. Due to the shorter season, Upper Division teams play two games a weekend.
If you are a young freshman who is playing in U14 and intend to try out for your high school team, you will be asked to play up in the U16 Division to avoid any overlap of seasons.