A professional bowler can still win a game with many gutter balls, but it would be challenging. The number of gutter balls thrown can significantly decrease the chances of getting a high score and winning the game.
However, a professional bowler typically has a high level of skill and experience and may be able to compensate for gutter balls by making high-scoring throws in other frames. Additionally, some professional tournaments have different rules and scoring systems that might allow a bowler to win despite having many gutter balls.