In the example with deficient soil, all parts of the plants should be equally deficient, so whether the chickens eat the vegetation or the roots will not matter. And where would the bugs and worms and other creatures get the missing minerals? They can't get them from the plants (which don't have enough), and they can't get them from rotting vegetation (which doesn't have enough) and they can't get them from the soil (which doesn't have enough).But, ranging chickens are likely to eat other things apart from plants. Even with the Ex Battery hens I now care for, vegitation is way down the list of feeding preference. They do eat some types of grass and a number of other plants. One would have to know the nutritional content of all the bugs, roots and other stuff they eat to make a valid judgement. This isn't really feasible.
So in that example, everything the chicken eats will be deficient in the same minerals. There will be no good source that the chicken can find, to make up the difference. So yes, the chicken will be deficient in the minerals, unless someone brings in a source of those particular minerals.