Yes, absolutely it will. But isn't the FX5 rated at 1000gph? If you keep it clean with regular maintenance, I see no reason it couldn't maintain the minimum 800 you need.
The other consideration though is head height - the lower the pump, the less GPH
it will move.
If you want to run a separate pump, eheim pumps are the quietest pumps out there that are commonly available. I am just not sure how you are going to hook it up without a sump, and without drilling the tank. It would be quite an eye soar in your display tank.