Nope, the supreme court ruled that a secret prison remains secret even if publicly known.
https://www.supremecourt.gov/opinions/21pdf/20-827_i426.pdf
"On appeal, the Ninth Circuit agreed with the District Court that much of the information sought by Zubaydah was protected from disclosure by the state
secrets privilege, but the panel majority concluded that the District
Court had erred when it dismissed the case. It believed that the state
secrets privilege did not apply to publicly known information.
...
Here, the
information held by the Ninth Circuit to be nonprivileged would necessarily tend to confirm (or deny) that the CIA maintained a detention
site in Poland. The Government has shown that such information — even if already made public through unofficial sources — could significantly harm national security.
...
Here, the state secrets privilege applies to the existence (or non-
existence) of a CIA facility in Poland, and therefore precludes further
discovery into all three categories of information the Ninth Circuit concluded to be nonprivileged.
...
This case is remanded with instructions to dismiss Zubaydah’s
current application for discovery under §1782. P. 18. "