Yes, Weakness Policy will activate.
Purifying Salt doesn't change any of the Ghost Type's actual properties when interacting with Garganacl. The ability halves the damage received from Ghost type attacks. This essentially allows Garganacl to take neutral damage from Ghost Type attacks, without the type itself dealing neutral damage, if that makes sense.
Source: I tested in an in-game Double Battle where my Tera Ghost Nacli took Super Effective damage from Hex and Weakness Policy activated.