Our breeder recommended Avoderm Puppy kibble. I noticed on the bag it says it has no wheat, soy or corn. So, should I avoid treats with these ingredients also? (We get our puppy next month) :)

Soy and wheat are common allergens. Corn can be, but it's pretty rare. More times than not, those ingredients are used as cheap fillers. That's not always the case, I feed a food that uses corn (Eagle Pack Original), but when you see a food with several different corn products or corn, wheat, and several grains, it's usually the sign of an inferior food.

The short answer is yes, but the long answer is not always. :D

With treats, I doubt the corn is used for omega-fatty acids or a digestible source of energy, so I'd probably find treats without them.

I usually use his kibble, marrow bones, or carrots as treats.

If your dog has no food allergies etc. it won't matter if the treats have grains in them. While I try to avoid excessive grains in their kibble, I let them have grains in their biscuits. While not the BEST treat, I do get Milkbones on occaison for them as a treat. Usually I keep the Canidae Snap Biscuits on hand.