Is icing your shoulders ever helpful if you have tendonitis?

YES. Ice after activity can reduce inflammation and help with soreness. Do not put the ice directly on the affected area; wrap in towel or plastic bag. In general do not ice for more thatn 15-20 minutes. Be awares the ice will numb the area and you give yourself frostbite (have seen it).
Ice pain. I've us a good simple way to reduce pain combined with stretching strengthening of other muscles NSAID and proper diagnosis.
Tendonitis. Ice can help certainly with acute injuries to help combat blood vessel dilatation and inflammation. More chronic tendinitis may be better treated with heat. For shoulders in particular you may want to consider heat before activity or exercises and ice following at 20 minute increments.