The primary apologetic value of the efficacy of God's word is obvious: the gospel is the power of God to save everyone who believes and the instrument the Spirit ordinarily uses to bring people to faith and keep and grow them in it. The implication for apologetic method is just as obvious: preach Christ, clearing out whatever bramble obscures a fuller and richer view of of him as you can.
I suppose if it is possible to "preach Christ from envy and rivalry" (Phil 1:15), it is also possible to do so without empathy. But, we are called to preach Christ "out of love," and love takes the questions people raise seriously, even when offered in the form of objections. And, as we have no doubt learned through wrestling with many of these same issues ourselves, the gospel constantly proves itself to be the best answer we have to each question we face. So, every question of this kind, properly considered in a spiritually realistic, empathetic, and intellectually serious way, is an occasion--invitation, really--to further preach Christ.
I say the gospel is the "best answer" because we do not always have the answer we or our neighbors may at first demand. Sometimes we even ask questions impossible for anyone to answer. But, in the gospel, we always have an answer sufficient for faith and life--an answer able to humble, silent, quiet, convert, correct, comfort, encourage, edify, and keep us. All of this belongs to the power of the gospel and is the primary apologetic value of the efficacy of God's word.
The power of God's word to accomplish these things, especially to bring people to faith and keep them in it, is also apologetically valuable in at least two secondary ways. This is an ancient point and here's how Origen, arguing "that the Scriptures are divinely inspired," makes it in De Principiis (written sometime prior to 225):
We may see . . . how that religion itself grew up in a short time, making progress by the punishment and death of its worshippers, by the plundering of their goods, and by the tortures of every kind which they endured; and this result is the more surprising, that even the teachers of it themselves neither were men of skill, nor very numerous; and yet these words are preached throughout the whole world, so that Greeks and Barbarians, wise and foolish, adopt the doctrines of the Christian religion (4.1.2).
The power of the gospel demonstrated in its fruitful advance among all kinds of people throughout the world, not just in the face of but through the means of the sometimes intense suffering of those who believe and the unskilled labors of a relatively few teachers, is astonishing. To Origen's mind, this is a very compelling apology for the faith.
It is no doubtful inference, that it is not by human power or might that the words of Jesus Christ come to prevail with all faith and power over the understandings and souls of all men. For, that these results were both predicted by Him, and established by divine answers proceeding from Him, is clear from His own words (4.1.2).
He then visits several places where Jesus taught that the gospel would go out and bear fruit throughout the world and that his disciples would suffer for their faith, before concluding that,
If these sayings, indeed, had been so uttered by Him, and yet if these predictions had not been fulfilled, they might perhaps appear to be untrue, and not to possess any authority. But now, when His declarations do pass into fulfillment, seeing they were predicted with such power and authority, it is most clearly shown to be true that He, when He was made man, delivered to men the precepts of salvation (4.1.2).
Origen's argument from the observed efficacy of the word of God, evident in the astonishing results of its preaching, argues to two entangled but distinct conclusions: (1) that the gospel is true and (2) that it possesses divine authority.
First, he argues that those results strongly support the truth of what Jesus taught since he predicted precisely what has come to pass. This can be understood somewhat narrowly, along the lines of prophet verification laid out in Deut 17:15-22, where a supposed spokesman for God would be tested by whether predictive words came to pass. Jesus passes this test; now we must pay close attention to everything he says.
It can also be understood in a broader sense, however. Those predictions speak more generally to the power of God's word to produce various kinds of effects. Predictions can be understood as singling out specific results to fix our attention not just on those specific outcomes but on the general efficacy of God's word which is evident all around us in the astonishing results it consistently produces. This is what Luther had in view when he spoke of drinking beer while God's word accomplished the Reformation.
I think if I could ask Origen whether he meant us to take his argument in the narrow or broad sense he would simply answer "Yes," meaning in both senses while implying the distinction was not an issue for him. Fair enough. But those who want to avoid the appearance of playing the dispensational parlor game of matching every cable news alert with some supposed predictive prophecy can still make good apologetic use out of the broader expectations Scripture clearly establishes. Besides, we have an even longer history of the global spread and saving power of the gospel to observe with perhaps even more astonishing results than Origen did. Here, the history of evangelical missions becomes a potent apology by way of the clear biblical expectation that the gospel is powerful to save and will ordinarily bear fruit everywhere it is preached.
According to Origen, however, if Jesus' message is not true then it could not possibly possess any authority, much less divine authority. And just because a word is true does not mean it has divine authority. So, the second conclusion he draws from the evident power of the word is that these astonishing results also demonstrate the divine authority of that word. Thus we have a second apology from the evident efficacy of God's word: not only is it true, but it has the ability to bring to pass or establish whatever it declares and foretells, up to everything God has appointed it to achieve in the world. Only a word spoken with divine authority has that kind of power over reality.