I know some AIO coolers have a port that you can fill it through but you're asking for air bubbles at thay point which ia death for one of these pumps.
I have refilled some asetek AIO's in the past because the tubes suck up the coolant and stuff grows in the loop after 5 years of use. The ones i have have all produced a buzzing sound that you can hear when near the case or it quiet, not much you can do about it as it's the nature of what looks to be a shaded pole motor driving the pump.
It wouldn't be impossible to replace the coolant and hoses and flush it out. It would be messy though. You are verging on creating your own custom water-cooling loop, especially if you decide to add a reservoir.
As long as the pump isn't the highest point in the system, you shouldn't have any issues with it having air in it.
Buy new? I personally wouldn't recommend an AIO... they just have too many points of failure for my liking, and many of the parts that fail can't be replaced like a fan on an air tower... high end air is on par with low/mid AIO and high end AIO is just so much more expensive that cost/performance doesn't really make sense. Also, as you've pointed out, pumps hum. A tower don't do that, 2 fans and it's whisper quiet.