Will nearby trenching harm my tree's roots?

As the tree grows, you might be able to prune the limbs near the wires to prevent contact. If the trunk of the tree grows in such a way that the wires are rubbing against it, you could put a protective guard on the wires. With the root issue, I'm afraid you won't be able to stop root growth. The tree will continue to develop and become larger so you might have to look at removing the tree and replant with another in a different location.