B767 cargo fire extinguishing systems are quite varied. None that I am aware of inhibit or alter in any way the cargo door operation.
Pressing the agent discharge button will do NOTHING unless the FWD or AFT cargo fire switch is first selected. This arms the bottles, closes the respective cargo heat valves, shuts down the recirc fans, sheds galley power aswell as silencing the fire bell. For the AFT cargo the lav galley vent fans are shut down and the packs inhibited from going to high flow mode.
On dual (bottle 1 and 2 discharge) a/c the bottles are fired individually by the crew. (I think these are non ETOPS)
On a/c with a single button, when the discharge button is pressed the first bottle is immediately discharged into the relevant cargo compartment and a 30 minute timer circuit is started after which time the second bottle (and 2A) is discharged into the compartment. Should the a/c land before the 30 minutes has expired then the second bottle will discharge on touchdown.
The extinguishant is halon (bromotriflouromethane) which is heavier than air, so be careful as you open the cargo doors as this will "fall" out. As a note the correct way to revive a person who has been overcome by halon is to invert them as much as possible so the inhaled halon literaly falls out of the lungs.