A Cup of Blood, a Cup of Blessing

The idea of a New Covenant has traditionally been seen as a uniquely Christian spin on Judaism, especially with that covenant sealed by blood.

Then he took a cup, and after giving thanks he gave it to them, and all of them drank from it. He said to them, “This is my blood of the covenant, which is poured out for many. - Mark 14.23-24

We know that the Qumran community envisioned itself as holder of a New Covenant, too.

...in accordance with the practice laid down originally by the men who entered the new covenant in 'the land of Damascus' - Damascus Document

Notice that - in this translation - Land of Damascus is in quotes. It does seem that this is a technical term of sorts that the community uses to designate its home in the wilderness, bt some have pointed out that Damascus may be translated, not as the proper name of a city in Syria, but as 'cup of blood.'
Whle this may be pushing a difficult translation too far, we cannot dismiss it out of hand.

IF Qumran did see itself bound by a covenant of blood, how does that affect the Christian use of the same symbol?