The simple answer: no.
The reasoning lies in how “ThruLines” are created. The following is from Ancestry’s description: “We use the family tree linked to your test to find people who are in your tree and are also in your matches’s linked trees. […]” In short, ThruLines searches the submitted family trees of your DNA matches to find lines that look like they match to your tree and then gives the listed ancestors to you as hints.
Ancestry also points out a serious issue with this program: “Since ThruLines are based on the family trees of you and other members of Ancestry, they’re as accurate as the trees they’re based on.” If someone adds an incorrect branch to one of your family lines, it will come back as a ThruLine, whether or not it is accurate.
In other words, the only thing ThruLines can “prove” (in the lineage society sense of the term) is that you share DNA with that user. They do not prove that you have ancestors in common. For that reason, you cannot use ThruLines as supporting documentation for a lineage society application.
Can you use DNA? Maybe. Each society has their own policies for the acceptance of DNA tests. The policy of the Daughters of the American Revolution can be found here. Be aware: most societies do not accept autosomal DNA tests, the type offered by most testing companies, or accept them only for the three most recent generations (applicant, parent, grandparents.)