A Wild Shaped Druid is not a valid target for Animal Growth Spell, even with this feat
The Animal Growth spell description specify that the target must be an animal (Gargantuan or smaller). Therefore only creatures with the animal type are valid targets, which is not the case of most of standards races available to the players (most of them are humanoid type).
The Wild Shape feature of the druid states:
This ability functions like the beast shape I spell, except as noted
The except as noted here part changes some duration, action cost or other details, but doesn't change anything about what I will now detail.
Beast Shape I is a spell of the Trasmutation school and Polymorph subschool. It is stated in the Polymorph rules that :
While these spells make you appear to be the creature, granting you a
+10 bonus on Disguise skill checks, they do not grant you all of the
abilities and powers of the creature.
Therefore as it isn't explicitly mentioned anywhere in the Beast Shape spell description or druid Wild Shape feature, the Wild Shape doesn't alter the druid creature type, it only makes him appear like an animal.
The feat Animal Soul states:
You can choose not to allow spells and effects to effect you if they would not be capable of affecting both your original creature type and the animal creature type.
This feat only allows to not be affected by some spells if they cannot affect both creature and animal types, which can be a useful defensive feature, but as for the Beast Shape and Wild Shape descriptions, it never intends to give the animal type. Hence having or not having this feat doesn't change anything to the situation.
Unless the druid in your group already is an animal (what I doubt), he doesn't qualify as a valid target for the Animal Growth spell, even while using Wild Shape.
Now even if this combination doesn't work, I'll answer your concern about multiple bonuses for AC and ability scores as this situation can happen in other circumstances.
An important rule to know about bonuses is:
Most bonuses have a type, and as a general rule, bonuses of the same type are not cumulative (do not “stack”)—only the greater bonus granted applies.
Very few bonuses types do stack with themselves (dodge bonuses for example), and if you have a doubt, you can check it on this page, on the bonus table. If it is not explicitly stated that a bonus stacks with itself, as for the dodge bonus, it doesn't. Untyped bonuses however, do stack with themselves.
Therefore if this combination of Wild Shape (based on the Beast Shape spell) and Animal Growth would have worked, as both Animal Growth and Beast Shape give size bonuses to ability scores and Natural Armor bonus to AC, they would not stack and the druid would benefit only of the higher bonus for each concerned ability score and for the AC.