No, a field ability will be accounted for once, and the effects cannot be stacked by having multiple Pokemon with the same ability. Imagine having a team full of Synchronize Kadabra, and expected a "300%" increase in meeting Pokemon with the same nature.
Not to mention that fact that the game wouldn't know which Kadabra to account for its nature, in this example. That's why the field abilities only apply to the Pokemon closest to the front of the party. All other "copies" are ignored.