Well i dont think so. Ive never had a problem with mine. It has a drain point, much like a radiator.
So when i change my oil, i drain the sump and the cooler all at the same time as i have mine V mounted down in between the radiator and sump.
And when i refill the system i just pour the oil into the motor and kick it over.
The oil pump does the work for you and the air bubbles will work their way out just like your coolant system.
I could say unbolt your cooler, disconnect the feed hose from your filter and fill it up that way, but that all depends on how accesible your oil cooler is and how much time you want to spend on changing oil.
Letting the oil pump do it for you should be fine.