This prompted me to look up what happened when Israeli troops took over the Rockefeller Museum that housed most of the Scrolls in 1967:
During the war, the Jordanians had fortified the Palestine Archaeological Museum and put gun emplacements in its main tower. The museum was strategically located outside the north-east comer of the Old City overlooking vital north-south roads in the Jerusalem area.
On June 6, Israeli paratroopers entered the building and secured it after feeble Jordanian resistance. One lieutenant—like most Israelis keenly interested in archaeology—immediately began to search for the Dead Sea Scrolls, but the display case was empty. Avraham Biran, director of the Israel Department of Antiquities, had received a call that same day from Carmella Yadin, Yigael Yadin's wife. She told him that Yadin had been notified that the museum would soon be in Israeli hands and asked if Biran would go to the museum and make sure that the scrolls and other antiquities were safe.
Biran needed no arm-twisting. He took two other archaeologists with him to the museum, where they were obliged to go in the back door, since the paratroopers were still engaged in a fire -fight in the front with Jordanians on the city walls.
Some of the paratroopers immediately conscripted Biran to give them, during the battle, an impromptu lecture and tour of the antiquities of the museum. The archaeologist was happy to oblige and led a few of the soldiers around the premises, with the sound of shooting and breaking glass coming from the front of the building. The next day, after the entire city had been secured, the paratroopers left. Some of them dutifully signed the guest registry as they filed out, complete with banal comments ("Fantastic," "Very pleasant").
In many ways, the Scrolls serve as a microcosm of the entire Israel/Arab conflict. During the 19 years that Jordan controlled the Scrolls, no Jewish or Israeli scholars were allowed to study them. Likewise, Jordan did not allow Israeli archaeologists to visit the Qumran site. Jordan made the scrolls Judenrein, just like the Old City of Jerusalem, Judea and Samaria.