Short answer: those parts of theology that are not irrelevant are ineffective.
The bulk of theology is concerned not with the existence of gods, but with the nature of particular gods, usually the God of Abraham. (That's one way to denote the deity worshipped by Jews, Christians and Muslims.) It works on the accepted premise of His existence most of the time, so that it can attempt to discern His wishes and therefore inform human behaviour.
If the existence of the god is the point in question, the premise is unsettled and any conclusions from this kind of inquiry are moot. Thus the vast majority of theology is useless to atheists and agnostics, as long as they maintain those positions.
The remaining theology which does attempt to establish the existence of the relevant god(s) is in a category known as philosophy of religion. This is the stuff which might be useful in a discussion between a believer and a non-believer. That's why every major argument this field has ever produced has already been thrown at atheists in the course of discussions and debates over the last few years.
Atheists cannot ignore philosophy of religion, because it's shoved in our faces at every opportunity. It's the source of such brain-twisters as the transcendental argument, the appeals to fear like Pascal's Wager and the it-must-have-happened interpretations of Resurrection accounts. This is theology's moment to shine, and all the big guns have come out.
So how's it doing? Not great. I'm happy to assert without posting statistics that atheism is increasingly common, especially among young people. Attendance at religious services is falling, and those churches which are growing are more often than not cannibalising the congregations of other churches. The big guns of atheism, Dawkins, Dennett et al, are not given a moment's pause by the apologetic hurled at them, and they can say exactly why in each case.
There are many religious folks who think, "If only they would read this particular book about God, they'd change their minds." If they haven't read the book, some eager evangelist has probably paraphrased it for them, and had a reply shot back.
The apparent reality is that theology-based apologetics have been completely exhausted, and have not found their target. The reassuring idea that atheists are only atheists because of their own ignorance disintegrates when you consider the constant, all-guns-blazing proselytism forcibly educating them from all sides.
If theology has something new to say that might actually affect this ongoing debate, it's not just sitting in the open and being ignored. It needs to be unearthed and brought to bear. Now.