I wouldn't worry about draining the rad; even if you do, coolant will still spill out everywhere when the pump comes off.
Open all the bleeders, then fill with the lisle funnel until coolant comes out the bleeders, close them, and run the engine with the lisle until the thermostat opens/fans come on with the heater on, BUT don't overfill with the Lisle since it needs room to expand. Fill the syetm so there isn't even any coolant in the funnel - just so you can barely see some at the top of the radiator or the bottom of the pressurized overflow tank.
In fact, having used mine so many times now, I drilled a vent hole in the lid and use it with the lid on because as the coolant gets to operating temp with no pressure in the system, it will start boiling in the funnel and occasionally blow out everywhere. LOL.