I see no problem with doing so because it has nothing do with the components inside of the computer its just a pump and two fans running, it doesn't even matter how you put it outside of the case too since rads are meant to be positioned differently in a case. You could even do this with only a PSU and aio if you have the proper adapters.
I know my aio (Kraken X61) uses a sata power connection to power the pump so unless you haven't opened your aio yet or something and you know what power connections it needs you seem good to go.
Other then that stuff, what aio are you using?
And why are you doing this? "To see if the pump will get the air out", you mean you think there's air trapped in the loop? If so then keep the radiator above the pump.
Other then that your pretty much set!