No! It's not one of the recovered cannon from the wreck site of Captain Cook's Endeavour.  A replica of those cannon, along with one of the anchors, is keep under lock and key in the Cooktown Museum.

Crazy as it may sound, this cannon, along with an officer to fire it, three cannon balls and two rifles, was sent to Cooktown in 1885 in response to an urgent request from the council to protect the citizens of Cooktown against a Russian invasion.

It can be found on the foreshore of the Endeavour River near Cook's Memorial.