Hey there! What I'll say here is based on my own experience and as someone who makes his own research, so by no means I'm a professional.
Muscle grows by causing it damage by lifting heavy weights. This damage is healed by making the muscle fibers bigger and stronger. Fitness is (or at least, should) all about having a healthy, all around balanced body, so SOME arm workout should be included.
As long it's very light exercise without heavy weights, you should be golden

also, keep in mind that diet is 80% of your results! Your trainer should be able to give you a diet plan for your goals. I do believe that you'll be recommended less protein and a bit more carbs but that's me guessing.