To answer the question directly, Christopher Hitchens is a visible example of at least a neo-conservative atheist, so no. There are obviously no atheists in the Religious Right, but there are other Rights.
The underlying accusation is that atheists deny gods to escape fear of capital-J Judgement.
I don’t deny that no longer believing in Hell is a relief. My conscience is as strong as ever, though, and if anything I try to be a more ethical person now than ever before. There is no god to guide my hand, so I must take full responsibility for my actions in a way one might not if one thinks God’s plan will take care of everything.
(Incidentally the main question is wonderfully nonsensical from an Australian perspective. Here, the capital-L Liberals are the main conservative party.)
I would like to respond to the text written under the actual question. Atheists, regardless of their political leanings, function from the same human base of morality as theists—a very important aspect of morality is to be aware of how your actions and decisions can cause harm to others. In other words, atheists do not just do something because it feels good, they also weigh the possible harmful/painful consequences for others in which their decisions and actions may result.
To the extent that “conservatism” includes, as one element, deference to religious traditions and institutions, atheists are not conservatives. But atheists can certainly be conservative in other ways. Many are fiscally conservative. Some are conservative on particular social issues – or even on social issues more generally – but of course, they will want reasons other than that the socially conservative position is favoured by words in a holy book or by the teachings of a religious body.
Many libertarians, who are often considered “conservative” on a range of issues to do with the role of government, are atheists.