Sharing communion without first baptizing a person is a small but common practice in the Episcopal Church right now. There's been a great deal of discussion on the question here on the Episcopal Café over the past few years.
(You can read an essay from 2007 here, and a series of three essays posted last year beginning with Part 1, and then Part 2 and Part 3.) These discussions generate more comments than any other subject on the Café. And now some of the ideas being discussed are going to be voted on at General Convention this summer.
The Diocese of Eastern Oregon has proposed a resolution that would remove any bar to anyone receiving Holy Eucharist. But it's not the only one.
"[There are] two resolutions on this topic [that] convention will consider when it meets July 4-12 in Indianapolis. The Diocese of North Carolina has proposed a longer-term look at the issue. Resolution C029 calls for a special commission to conduct ‘a study of the theology underlying access to Holy Baptism and Holy Communion’ and recommend to the 78th General Convention any amendment to Canon 1.17.7 it believes is needed.
The texts of both resolutions are available here. Eastern Oregon’s is accompanied by a diocesan statement explaining its stance.
This will be the second time in recent years that what is variously called open communion, open table and communion of the non- or unbaptized has come to convention. In 2006, the General Convention affirmed Canon 1.17.7 (via Resolution D084) and asked for the House of Bishops Committee on Theology and the Standing Commission on Liturgy and Music to provide to the 2009 meeting of convention ‘a pastoral and theological understanding of the relationship between Holy Baptism and eucharistic practice.’"
Mary Frances Schjonberg has collected a huge compendium of resources in an article posted on the Episcopal News Service this afternoon. It turns out that this controversy has been discussed to one degree or another since at least 1982 in the Episcopal Church. The discussion in church history goes all the way back to Didache, written in the first centuries of the Church's life.
Schjonberg's article contains links to all the original Episcopal Church material such as previous resolutions, Ecumenical statements and position papers.
You can find the whole history of the Episcopal Church's Communion without baptism discussion here. If you're preparing for General Convention, this is some must reading.