I agree with the answers above regarding bike fit, position, etc.
However, depending on what type of cycling you are doing, if you are new to the sport, etc, the answer may be yes.
If you are doing terrain or downhill mountain biking, then your arms and shoulders can get sore from the reverberations and trying to maintain your balance and stability. If you’re doing triathlon and have yourself in an aero position, then you’re placing a lot of pressure on your arms and shoulders. They may not be used to that position. Any new change can cause soreness. If you’re new to cycling, racing, duathlons, triathlon, etc, your bike position is more forward than a regular, recreational road bike. Your body needs to adjust to the forward motion of your body. A good cycling training program will include upper body to strengthen your chest and upper back to support your body in a isometric contraction for the duration of your race.
However, if you’re cycling for recreation, on a stationary bike or a spin class, then no. Those bike are made where your upper body is not in a supportive role while you are cycling.