With any cargo fire; Main Deck, Lower AFT or FWD, each have a specific checklist to complete. None of which calls for pulling the smoke removal handle.
Only an unknown source of smoke/fire would require the Smoke, Fire or Fumes checklist, and from this checklist, if smoke is the greatest threat, would the crew be directed to the smoke removal checklist. Only if the source of the smoke was determined to be from the flight deck, would the crew then pull the smoke removal handle.
For a main deck cargo fire, arming the Main Deck cargo fire switch shuts off two packs (2&3), and E/E switches to closed loop. When the Depress switch is pushed, the cabin depressurizes to 25000', and the aircraft descends or climbs to 25000'.
Not only does this starve the fire, but also maintains zero pressure differential on the main deck, with Pack 1 providing a slight positive pressure for the Upper deck. This logic is what keeps the smoke from the Upper deck. Had pack 1 not tripped, and Pack 3 not been selected OFF(per the checklist at the time), they probably would have had at least a little extra time before the fire/smoke breached the FLT deck.
This is also why the E/E has to go to closed loop, not override like the FWD and AFT lower deck. If override were selected, with no differential pressure, E/E cooling would be lost.