Just as with paper genealogy research, we must start with the known (the living woman who tested her mtDNA) and work back generation by generation.
To expand on RJ's comment...
Priscilla Alden's mother is identified as Alice Mullins (Unknown-259877), but Alice's mother - who is Priscilla's maternal grandmother from whom she inherited her mtDNA is unidentified. Also unidentified is the mt DNA from Priscilla, Alice and Alice's mother. Could it become identified? Maybe.
Priscilla is shown on the tree as having six daughters. Each of them passed the mtDNA to their daughters ect. If you could trace the decendents of each of them to the present day through an unbroken matrilineal line and a few of the descendent women are willing to test, then you might be able to acertain the mtDNA for Priscilla et al.
Alice Mullins (Unknown-259877) has three daughters in addition to Priscilla shown on this tree. IF you were able to trace the matrilineal descendents of each of the sisters to a living woman who was willing to test, they would also be carriers of the same mtDNA.
IF you were to research and identify Priscilla's matrilineal grandmother and the grandmother's sisters and mother, the same tracing to living women to be tested could also be made.
Once Priscilla's mtDNA is identified, then you could contact the testers and ask to compare your results. IF they match, you would still need to continue researching your matrilineal ancestors and those of Priscilla until you find the common maternal ancestor that started the mtDNA chain.
It would be a lot of research and we don't know if records exist to substantiate the identification of the common ancestor, should one be presumed to exist from the DNA comparison. On the spectrum of possibilities, I think this would technically be possible but the probability of identifying the connection without exhuming bodies or finding a rare cache of previously unknown documents is slim.