Is a parthenogenetic female a ‘group of one’?

A few weeks ago John Wilkins wrote a long and thoughtful 5-part review of a recent paper by E.O.Wilson and D.S.Wilson:
The two Wilsons on sociobiology
Sociobiology 2: Theoretical foundations
Sociobiology 3: Kin selection and pluralist explanations
Sociobiology 4: individuals as groups, and a summary
Sociobiology 5: What is at issue
Since I always thought of group selection in the Unto Others sense of the term, I am not as confused as some others who are familiar with some older, unrealistic models. I still think that the best explanation is by Robert Brandon in, I think, fifth chapter.
Sexual reproduction is a pretty important component of hierarchical view of units/levels of selection, so one may wonder how parthenogenesis (virgin birth) affects that theoretical construct. Here are some recent thoughts on parthenogenesis:
Sandra Porter: Did she or didn’t she? Genetic testing and virgin birth
RPM: What’s the deal with ‘virgin birth’ (parthenogenesis)?
Greg Laden: The Bible as Ethnography ~ 05 ~ The Virgin Birth
Martin Rundkvist: Sacred Parthenogenesis
Zuska: Are Men Necessary? ‘Ask a Science Blogger’ Wants To Know!
Anne-Marie: Gynogenesis redux: Return of the Clones (and earlier: Hybridogenesis: Who’s your daddy? Who cares! and Gynogenesis: Attack of the clones)
Now you put the two topics together….mind boggles.