yeah...you should be able to screw the brass adaptor in the faucet and then screw the hose right on to it and fill the tank.... I drain my tank out the door into the back yard so I never use it to drain.
Only problem hooking it right to the faucet to fill will be adjusting the water temp ....with the adaptor I leave it on drain and use a digital thrometer to adjust the water temp the same as my tank water....without it might get pretty tricky unless you can figure out where your faucet handles need to be to get the temp pretty close....or use a thrmometer at the fill end as it is going into the tank and make adjustments as needed to get it close before it gets too full.
I always hook it up and then put the end that the water comes out into the sink and get the water temperature perfect there before taking it to the tanks. My question is.... how do you drain it out the door? I know with my normal hose you have to get the hose completely filled with water before it will flow. Is that what you have to do? Quite frankly, that would be a PITA to get the 25' python hose full of water to start suction. Unless, of course, you hook it to the faucet first to fill it with water and then unhook it and set it outside. That too seems like it'd be a PITA though.