pelochas, that is correct a closed loop is fully enclosed plumbing. The water never leaves plumbing except when its in the pump chamber itself. In the closed loop you would need either a bulkhead drilled in the back of the tank or make up a U shaped inlet that takes water up and over the top of the tank. This inlet would need to have a fitting at the top most point with a screw cap so you can prime the pump. The inlet would have to be below water line enough that it would never become exposted to air to break the syphon once the pump is primed. Water then goes in the inlet and directly to the pump and then out the pump directly into plumbing again back up to the tank.
A standard hang on oveflow with a 1" drain should be able to process up to 700GPH flowrate depending on how its plumbed to the sump. If your pump is pushing more than this at the given head height you will have a problem so its best to either get a second overflow or throttle back your pump with a ball valve on the outlet side. Also note that the pumps output is not constant at different heights. As the pump has to push water up it will output less water. So your 1200GPH pump at 0' head may only output 1000 or less GPH
at 4' head. Reference the pump box or manufacturers website for a flow diagram on how head affects the pumps performance.