Do Christian concepts of fellowship allow for a congregation to welcome atheists to participate in their community?

Of course it isn't wrong to fellowship with other human beings. Just remember that it may take some time to find a group who feels the same way, but it will be worth it. Look for the enlightened ones who welcome you with open arms.

A Catholic Official Position

Catholics absolutely welcome atheists or anyone else to attend Holy Mass. Unfortunately, as suggested elsewhere, we do not feel it is appropriate for most non-Catholics to receive Holy Communion. For example, a norm developed by the National Conference of Catholic Bishops (later the U.S. Conference of Catholic Bishops) reminds its readers of the Catholic belief that "the celebration of the Eucharist is a sign of the reality of the oneness of faith, life, and worship", and states:

We also welcome to this celebration those who do not share our faith in Jesus Christ. While we cannot admit them to Holy Communion, we ask them to offer their prayers [or, if one does not believe in the efficacy of prayer, simply their hopes and thoughts] for the peace and the unity of the human family.

(emphasis added)

It is often the case, for a few possible reasons, that even a practicing Catholic attending Mass will not receive Holy Communion either; so one who is not Catholic, Christian, or even theist should not feel left out.

From the point of view of a Seventh-Day Adventist, we welcome unbelievers, because many in the church have come from Atheism. You would be welcome with open arms.

In the Christian and Missionary Alliance Church (C&MA) of which I am a member, you would definitely be welcome when attending almost any gathering of church members, whether large or small, plenary or small group.

Our church has "ministries" for almost every age group and for almost every conceivable interest or need (e.g., divorce recovery, 12-step meetings for a variety of addictions, senior citizens, college and career, single parents, grief counselling, church membership classes, growth groups, and many more).

Even if you are simply a disinterested observer, or are there to enhance your social life, you would be welcomed, accepted, and loved.

Does this mean you are therefore free to "sow seeds of discord," or to proselytize, so to speak, for atheism? Of course not. Honest, open, and even heated discussions are encouraged in my church, but as in most every place besides church (except the Jerry Springer show!), good manners are de rigueur.

Does this mean that every C&MA church will be as equally welcoming? Probably not. Despite a shared denominational identity, each local church within the denomination has its own culture, norms, mores, and folkways. Rest assured I am not making excuses for churches in my denomination which are not as accepting of atheists (for example), but I'm just being realistic about regional and cultural differences, whether in the US or abroad.

By the way, I'm familiar with one local church in the Episcopalian denomination which has an Alpha Course for seekers who are interested in finding out more about the Christian faith. Who knows, there you might even meet another nonbeliever of the opposite sex with whom you can strike up a friendship!

In conclusion, all local Christian churches should--ideally--be welcoming of strangers and non-members, but we live in a far from ideal world. Nevertheless, I encourage you to seek out a local church which has an open door policy and welcomes seekers of all stripes, even atheists. When you find one, however, do not expect perfection, just a bunch of imperfect Christians, all of whom are under construction. In other words, be willing to show the same respect, courtesy, and patience they show to you.

Do Christian concepts of fellowship allow for a congregation to welcome atheists to participate in their community?

In the most general terms, yes - most congregations are open to non-member participation. Saying that, it is possible different congregations have a nuanced stance in this regard - some of their meetings may be closed and it is best to ask the leaders of an individual community what their stance is. Another consideration is that while a particular meeting may be open to non-members, some of the practices engaged in may be restricted to member (or visiting Christian) participation - e.g. taking Holy Communion - so your participation may be partial in that respect (as would be appropriate considering you would not believe all that the congregation members believe with respect to those practices).