It is evident that muscle growth happens through exercise. This article, Muscle growth and exercise explains that there are three mechanisms involved:
- by an increase in muscle cell numbers,
- by an increase in muscle fiber diameter, and
- by an increase in fiber length.
So, your question is whether the first mechanism is affected by exercise. The others are not related to the count of the cells, but how large each cell is.
The abstract goes on to explain:
Growth in cell numbers is limited to the prenatal and immediately postnatal period, with the animals and man being born with or soon reaching their full complement of muscle cells.
So, the answer to the question is no, exercise does not increase the number of muscle cells.
Exercise does, however, increase muscle mass, by increasing the size and count of the components that make up each cell:
Thus, growth occurs by either hypertrophy of the existing muscle fibers by adding additional myofibrils to increase the muscle mass or by adding new sarcomeres to the ends of the existing muscle fibers to increase their length. Both of these mechanisms occur during the growth process. Growth in the girth of the muscle fibers appears to take place by splitting of the myofibrils. This may be stimulated by development of stress creating an unequal pressure with splitting at the Z-band and development of additional SR and T-tubule systems. This adds to the diameter or girth of myofibers without any hyperplasia. The growth in length occurs at either end of the fibers and results in addition of new sarcomeres. In both cases, new myofibrillar protein must be synthesized and deposited in the muscle cells.
What determines adding sarcomeres and myofibrils?
You guessed right: Exercise.
Exercise stimulates the increase in myofibrils which increase the overall size of muscle cells.
Well exercised muscles can not only add more size but can also develop more mitochondria, myoglobin, glycogen and a higher density of capillaries.
Nutrition (especially protein intake) also plays an important role in muscle growth, but growth cannot occur without exercise.