To some extent, yes! It does play an important role to keep your game at a high level. For example, a tall player can perform a service or return of serve with more power and better angle. However, it is not the only factor to be successful in tennis because tennis is not only about serving.
The most important thing is your skill. Because the history of tennis is full of short tennis players who dominated it at their peak. Felicisimo Ampon is a great example who was considered the best player in the past while being only 4 feet 11 inches tall.