I have a player who is a druid. They naturally are interested in obtaining armor with the wild special property. They have argued that when they wild shape and their gear melds into their bodies that the armor check penalties do not apply. After carefully reading the druids wildshape ability, beast shape, elemental body, plant shape, wild armor property, and transmutation (polymorph), none of them are clear about this.
Beast shape/elemental body/plant shape had no real useful information except the polymorph subschool. The polymorph subschool however did mention
When you cast a polymorph spell that changes you into a creature of the animal, dragon, elemental, magical beast, plant, or vermin type, all of your gear melds into your body. Items that provide constant bonuses and do not need to be activated continue to function while melded in this way (with the exception of armor and shield bonuses, which cease to function). Items that require activation cannot be used while you maintain that form.
Note that it mentions nothing about the weight of the items being carries no longer applying, so assuming your strength does not change when you wildshape, if you were encumbered then, you will be encumbered after because the weight/mass is still there.
The wild property allows armor and shields to apply its armor bonus (which means that shields gain nothing except their enhancement bonus).
So, the weight does not disappear, but your melded items for the most part become ineffective and inaccessible. It directly states that the armor and shield bonuses cease to function but mentions nothing else about armor traits. To me this means that the armor check penalty, arcane failure chance, and even movement reduction should all still exist