No, players on an MLB 40-man roster cannot play during a work stoppage or strike, even if they are optioned to the minor leagues. [1, 2]
Why 40-Man Roster Players Cannot Play
Union Membership: Every player on a 40-man roster belongs to the Major League Baseball Players Association (MLBPA), which means they participate in the strike or are locked out by owners. [1, 2]
Major League Contracts: Because their contracts are Major League-level agreements, they are barred from team facilities, games, and official workouts during a stoppage. [1, 2]
Minor League Status Doesn't Matter: A player can be physically stationed at Triple-A or Double-A, but if they occupy a spot on the 40-man roster, they are sidelined alongside the major leaguers. [1, 2]