The answer to the first question is clearly yes. The existence of ‘secular’ political parties and lobby groups is evidence enough that atheists are mobilizing in the political sphere and bringing their atheistic ideals with them into the fray. Atheism can be (and is) political. This paper, on a contemporary political theory website shows that “New Atheism” (or “aggressive atheism’, as the author call it) has already entered the radar screens of at least some modern political theorists.
The answer to the second question, however, is not so simple.
I suppose, from one perspective, the idea of atheism can be understood as a nearly non-political concept. After all, atheism can be defined simply as the absence of belief in god or gods. Beyond theocracy and separation of church and state issues, atheism thus defined has little to say about how a country is run.
Can atheism be the foundation of a coherent and comprehensive political ideology? Well, by itself, not really. Just as belief in a god alone cannot create a comprehensive ideological system without accompanying religious texts, institutions, dogmas, etc. Atheists must therefore draw upon more than just disbelief in god if they desire to create an ideology that can meet the demands of contemporary society.
Atheists have a wealth of opportunity before them with regards to becoming political. Rejecting the theistic paradigm allows atheists to discard poorly constructed beliefs in favor of better substantiated claims, at least where deities are concerned. But how can atheists decide upon fiscal and monetary policy? What about foreign and domestic policy?
Something that I think would appeal to most, if not all atheists, is the idea of an evidence- and reason-based approach to almost everything political. This implies a healthy skepticism and a disposition towards empiricism, as well as careful philosophical consideration where necessary (i.e. ethical problems). An aspiring atheist politician could draw upon the best evidence and knowledge available from the fields of science and social science to inform their policies. Moral problems could be tackled using the best philosophy available.
For example, in response to the economic assertion: “We need to cut government spending because otherwise inflation will result” an atheist politician could respond: “alright, fair enough, but what is the latest economic data on the subject? What has happened in the past in similar situations? What do the leading economic schools of thought have to say about inflation and cutting government spending?”
In response to the moral assertion: “abortion should/should not be allowed”, an atheist politician could draw upon the latest scientific evidence regarding abortion procedures and fetus/embryo biology, and consult with various ethics systems to determine the morality of abortion.
In response to the foreign policy assertion: “We need to invade Iraq because there are WMD’s there” an atheist politician could ask “What is the evidence for this assertion? Furthermore, how certain are we that, if these WMD’s exist, they pose a reasonable threat to us, given our military capacity?”.
So, in summary, atheism cannot form a coherent ideology without the aid of other concepts and ideas. The basis of an ideology with atheism (or secularism) as a central tenet could be empiricism and skepticism. Atheists could draw upon the best evidence and knowledge available from the sciences and social sciences. To answer moral questions, atheists may consult with philosophy and ethics.
The last question (are there any benefits to atheism entering the political sphere) is certainly yes, at least, for atheists. If atheists wish to have their worldviews represented in the political institutions of our time, they need to mobilize. Getting politically active is the first step towards having a say in the outcomes of your country. Being active and visible is far better than being submissive and passive. Albeit being active in the wrong ways can be damaging, and any nascent atheist political movement or politician must be tremendously careful where they tread.
If implemented correctly, I think an ideology with atheism as a central tenet could be tremendously powerful. The demon-haunted world could finally be dispelled where it has for so long held bastion: in the seats and halls of government.