In a word: no.
First of all, “proof” in the genealogical sense is the coalescence of all the information relevant to the determination of an answer to a question, the analysis of that information (generally the determination of its reliability), and the synthesis of the information and analysis into a clear and coherent argument.
Membership in a DNA Circle at AncestryDNA for a specific ancestor might (at the very best) be considered potential evidence of a relationship. It’s important to remember how any two people get into a DNA Circle at AncestryDNA:
- they share an amount of DNA significant enough to indicate a biological relationship
- they have the same (or very similar names) in their tree–names that appear to be the same person
Membership in a tree is not “proof” in the truest sense of the word–at least from my perspective. Two individuals are related (hence the DNA connection). But just because they share the same (or very similar) ancestors in their tree does not mean that the connection has to be through those “shared” ancestors. The “circle membership” process does not analyze the accuracy of the genealogical connections in their tree.
Circle membership at AncestryDNA is a clue to research further. Because the circle membership is automated, my personal take is that it should not be used as “hard proof.”