Yes, it is absolutely relevant.
The details of the warfare have changed, and the political battles are different. However, to see how it is relevant, look at the things that haven't changed. Men still go to war, and still have to choose between safety and glory (Achilles' choice). Women still watch their men go off to war (and now men watch their women go too). Fathers still weep over lost sons, and friends over lost friends, and so on.
The motives and the emotions stay relevant, as well as the elements of fate and related to death.
The Iliad is extreamly relevant to our time. There are many, but perhaps the greatest connection lies in the motive for the inevitable war that ensues. The "petty" factor must not be over looked. You have the various characters pride playing a huge role in the choices, direction and outcome of the war. Take Achilles and Agamemnon's opening quarrel for starters. Essentially that argument is over nothing more than "who is the bigger, man". It is bullies at their best. Yet all it took was one going too far with the name calling and slander to go to the point of no return. Even when great men, in some cases wiser men, were advising against the verbal sparing. Another example of this wounding pride is Hector's need to stay and fight Achilles even though he knows he will not win. He is too ashamed to go back to Troy and admit that he should have retreated after Patroclus was slained and not have let it come to this. Patroclus himself chose to fight in a war he was not ready for because he was angered by Achilles arrogance. The moments are many in this epic poem. Botton line; the suffering of many Achaeans and Trojans occured because of the choices of men thought to be better, braver, wiser, and above pride, and greed. Is this not the cry of the American people at a time when their economy and well being is placed in the hands of greedy, arrogant,a nd prideful politicians?