Basic physics teaches us that to throw a ball at your top velocity you must use more than just your arm. You must use the entire kinetic chain, along with every muscle group that will help you reach your top velocity. There are countless articles on this site on how to use more of your body to increase pitching velocity and there is also the revolutionary pitching velocity program called 3X Pitching to coach and train you how to pitch with your total body and increase pitching velocity from 5-10 mph. Outside of this information let's go into more detail on arm strength and pitching velocity.
Arm Strength and Pitching Velocity
To answer the question, YES, more arm strength will increase pitching velocity but it could prevent you from reaching your potential top velocity. The arm muscles that are responsible for generating arm speed is the Pectoralis major, Subscapularis, Supraspinatus, Infraspinatus, Teres minor and Latissimus dorsi. Technically these are not arm muscles because they are more apart of the shoulder, but these muscles are responsible for moving the arm. This is one of the problems with using the phrase "arm strength" when talking about throwing velocity.
Conditioning these muscles to grow stronger and faster will increase pitching velocity but it is a double edge sword. It would be like a sprinter strengthening his arm muscles to increase his running speed. This will help in the beginning but it will eventually have a counter effect. The counter effect is in the kinematics. When the upper body becomes the more dominate force, then it drives the rest of the kinetic chain. This would mean if the sprinters dominate force is coming from his swinging arms, then his legs will be conditioned to grow more passive. This would have a counter effect on increasing speed because the legs have more potential to generate speed than the arms. The reason for this is that the legs are pushing off of the ground and they have bigger muscle groups to do this more explosively. This applies to pitching because pitching is a similar explosive movement. The only difference in pitching is that the explosive movement of the body must then transfer into the velocity of the ball. If a pitcher focuses mainly on "arm strength," he will see a bit of an improvement initially, but it will eventually start to work against him. This is because the kinematics, or pitching mechanics, are changing. The arm is becoming more of the dominate force and the legs are becoming more passive. Just like sprinting, the legs will have a bigger impact on building power and velocity.
The lesson here is that these arm muscles must grow stronger to increase pitching velocity, but they also must not be the dominate force when generating pitching velocity. The foundation of a velocity focused training program must be built around leg and core lifts. The upper body or arm lifts must be a part of the program, but not the main focus. The Fusion System in the Ace Pitcher handbook, which is apart of the 3X Pitching Velocity Program, is a perfect model of this approach.
Every single pitcher who starts the 3X Pitching Velocity Program has this issue. Their upper body is the dominate force in generating their pitching velocity, which is limiting their potential. Once they reverse their kinematics their pitching velocity begins to increase again. This reverse engineering is training them to use the legs as the dominate force and the arms as an elastic reaction to that force. You will see these type of kinematics with pitchers like, Tim Lincecum, Aroldis Chapman, Flex Hernadez. This type of approach to pitching mechanics will not only increase pitching velocity, but it will also help reduce injury to the arm. This is because the arm is now being used as an elastic tool instead of a flexed contractile force to generate pitching velocity.